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\advance\labelwidth-\labelsep} +\def\@listvi {\leftmargin\leftmarginvi + \labelwidth\leftmarginvi + \advance\labelwidth-\labelsep} + +% create title +\providecommand{\maketitle}{} +\renewcommand{\maketitle}{% + \par + \begingroup + \renewcommand{\thefootnote}{\fnsymbol{footnote}} + % for perfect author name centering + \renewcommand{\@makefnmark}{\hbox to \z@{$^{\@thefnmark}$\hss}} + % The footnote-mark was overlapping the footnote-text, + % added the following to fix this problem (MK) + \long\def\@makefntext##1{% + \parindent 1em\noindent + \hbox to 1.8em{\hss $\m@th ^{\@thefnmark}$}##1 + } + \thispagestyle{empty} + \@maketitle + \@thanks + %\@notice + \endgroup + \let\maketitle\relax + \let\thanks\relax +} + +% rules for title box at top of first page +\newcommand{\@toptitlebar}{ + \hrule height 2\p@ + \vskip 0.25in + \vskip -\parskip% +} +\newcommand{\@bottomtitlebar}{ + \vskip 0.29in + \vskip -\parskip + \hrule height 2\p@ + \vskip 0.09in% +} + +% create title (includes both anonymized and non-anonymized versions) +\providecommand{\@maketitle}{} +\renewcommand{\@maketitle}{% + \vbox{% + \hsize\textwidth + \linewidth\hsize + \vskip 0.1in + \@toptitlebar + \centering + {\LARGE\sc \@title\par} + \@bottomtitlebar + \textsc{A Preprint}\\ + \vskip 0.1in + \def\And{% + \end{tabular}\hfil\linebreak[0]\hfil% + \begin{tabular}[t]{c}\bf\rule{\z@}{24\p@}\ignorespaces% + } + \def\AND{% + \end{tabular}\hfil\linebreak[4]\hfil% + \begin{tabular}[t]{c}\bf\rule{\z@}{24\p@}\ignorespaces% + } + \begin{tabular}[t]{c}\bf\rule{\z@}{24\p@}\@author\end{tabular}% + \vskip 0.4in \@minus 0.1in \center{\today} \vskip 0.2in + } +} + +% add conference notice to bottom of first page +\newcommand{\ftype@noticebox}{8} +\newcommand{\@notice}{% + % give a bit of extra room back to authors on first page + \enlargethispage{2\baselineskip}% + \@float{noticebox}[b]% + \footnotesize\@noticestring% + \end@float% +} + +% abstract styling +\renewenvironment{abstract} +{ + \centerline + {\large \bfseries \scshape Abstract} + \begin{quote} +} +{ + \end{quote} +} + +\endinput diff --git a/papers/Collabra/cover_letter.Rmd b/papers/Collabra/cover_letter.Rmd new file mode 100644 index 000000000..700385be2 --- /dev/null +++ b/papers/Collabra/cover_letter.Rmd @@ -0,0 +1,27 @@ +--- +output: pdf_document +--- + +Dear Editors, + +We are pleased to submit this paper to *Mathematics*, for the special issue "Advances in Statistical Computing". + +The paper, titled "Check your outliers! An accessible introduction to identifying statistical outliers in R with *easystats*", provides an overview of current recommendations and best practices regarding the diagnosis and treament of outliers. It demonstrates how these recommendations can be easily and conveniently implemented in the R software using the *{performance}* package of the *easystats* ecosystem. The manuscript covers univariate, multivariate, and model-based statistical outlier detection methods, their recommended threshold, standard output, and plotting method, among other things. + +In this sense, the paper fits very well with the special issue "Advances in Statistical Computing", as it essentially communicates to the wider public current advances in the statistical computing of outlier detection algorithms and their implementation in currently available open source and free software. This makes the manuscript relevant to data science, behavioural science, and statistical computing more generally. + +Our current submission is original and has been neither published elsewhere nor is currently under consideration for publication elsewhere. All authors have contributed substantially to the software and manuscript. All authors gave final approval to the manuscript and accept to be accountable. We have no conflicts of interest to disclose. + +We would also like to use the open peer review option. + +Thank you for considering our submission. + +Best Regards, + +Rémi Thériault + +Department of Psychology, + +Université du Québec à Montréal, + +Montréal, Québec, Canada \ No newline at end of file diff --git a/papers/Collabra/mybibfile.bib b/papers/Collabra/mybibfile.bib new file mode 100644 index 000000000..463fd9e2b --- /dev/null +++ b/papers/Collabra/mybibfile.bib @@ -0,0 +1,162 @@ +@article{leys2019outliers, + title = {How to Classify, Detect, and Manage Univariate and Multivariate Outliers, With Emphasis on Pre-Registration},author = {Leys, Christophe and Delacre, Marie and Mora, Youri L. and Lakens, Daniël and Ley, Christophe}, + journal = {International Review of Social Psychology}, + year = {2019}, + doi = {10.5334/irsp.289} +} + +@article{leys2013outliers, + title = {Detecting outliers: Do not use standard deviation around the mean, use absolute deviation around the median}, + author = {Christophe Leys and Christophe Ley and Olivier Klein and Philippe Bernard and Laurent Licata}, + journal = {Journal of Experimental Social Psychology}, + volume = {49}, + number = {4}, + pages = {764-766}, + year = {2013}, + doi = {10.1016/j.jesp.2013.03.013}, + url = {https://doi.org/10.1016/j.jesp.2013.03.013} +} + +@article{leys2018outliers, + title = {Detecting multivariate outliers: Use a robust variant of the Mahalanobis distance}, + journal = {Journal of Experimental Social Psychology}, + volume = {74}, + pages = {150-156}, + year = {2018}, + issn = {0022-1031}, + doi = {10.1016/j.jesp.2017.09.011}, + url = {https://www.sciencedirect.com/science/article/pii/S0022103117302123}, + author = {Christophe Leys and Olivier Klein and Yves Dominicy and Christophe Ley}, +} + +@article{simmons2011false, + author = {Joseph P. Simmons and Leif D. Nelson and Uri Simonsohn}, + title ={False-Positive Psychology: Undisclosed Flexibility in Data Collection and Analysis Allows Presenting Anything as Significant}, + journal = {Psychological Science}, + volume = {22}, + number = {11}, + pages = {1359-1366}, + year = {2011}, + doi = {10.1177/0956797611417632}, + URL = {https://doi.org/10.1177/0956797611417632}, +} + +@Article{easystatspackage, + title = {easystats: Framework for Easy Statistical Modeling, Visualization, and Reporting}, + author = {Daniel Lüdecke and Mattan S. Ben-Shachar and Indrajeet Patil and Brenton M. Wiernik and Etienne Bacher and Rémi Thériault and Dominique Makowski}, + journal = {CRAN}, + year = {2022}, + note = {R package}, + url = {https://easystats.github.io/easystats/}, + } + +@Article{ludecke2021performance, + author = {Daniel Lüdecke and Mattan S. Ben-Shachar and Indrajeet Patil and Philip Waggoner and Dominique Makowski}, + title = {{performance}: An R package for assessment, comparison and testing of statistical models}, + volume = {6}, + number = {60}, + journal = {Journal of Open Source Software}, + year = {2021}, + pages = {3139}, + doi = {10.21105/joss.03139}, + url = {https://doi.org/10.21105/joss.03139} + } + +@Article{patil2022datawizard, + title = {{datawizard}: An {R} package for easy data preparation and statistical transformations}, + author = {Indrajeet Patil and Dominique Makowski and Mattan S. Ben-Shachar and Brenton M. Wiernik and Etienne Bacher and Daniel Lüdecke}, + journal = {Journal of Open Source Software}, + year = {2022}, + volume = {7}, + number = {78}, + pages = {4684}, + doi = {10.21105/joss.04684}, + } + +@article{cook1977detection, + author = {R. Dennis Cook}, + title = {Detection of Influential Observation in Linear Regression}, + journal = {Technometrics}, + volume = {19}, + number = {1}, + pages = {15-18}, + year = {1977}, + publisher = {Taylor & Francis}, + doi = {10.1080/00401706.1977.10489493} +} + +@book{iglewicz1993outliers, + title = {How to detect and handle outliers (Vol. 16)}, + publisher = {Asq Press}, + author = {Iglewicz, B. and Hoaglin, D. C}, + year = {1993} +} + +@article{gnanadesikan1972robust, + title = {Robust estimates, residuals, and outlier detection with multiresponse data}, + author = {Gnanadesikan, R. and Kettenring, J. R}, + journal = {Biometrics}, + pages = {81-124}, + year = {1972} +} + +@article{hubert2018mcd, + author = {Hubert, Mia and Debruyne, Michiel and Rousseeuw, Peter J.}, + title = {Minimum covariance determinant and extensions}, + journal = {Wiley Interdisciplinary Reviews: Computational Statistics}, + volume = {10}, + number = {3}, + pages = {e1421}, + doi = {10.1002/wics.1421}, + url = {https://doi.org/10.1002/wics.1421}, + year = {2018} +} + +@article{tukey1963less, + title={Less vulnerable confidence and significance procedures for location based on a single sample: Trimming/Winsorization 1}, + author={Tukey, John W and McLaughlin, Donald H}, + journal={Sankhy{\=a}: The Indian Journal of Statistics, Series A}, + pages={331--352}, + year={1963}, + publisher={JSTOR} +} + +@article{van1995statistical, + title={Statistical mimicking of reaction time data: Single-process models, parameter variability, and mixtures}, + author={Van Zandt, Trisha and Ratcliff, Roger}, + journal={Psychonomic Bulletin \& Review}, + volume={2}, + number={1}, + pages={20--54}, + year={1995}, + publisher={Springer}, + doi = {10.3758/BF03214411} +} + +@article{ratcliff1993methods, + title={Methods for dealing with reaction time outliers.}, + author={Ratcliff, Roger}, + journal={Psychological bulletin}, + volume={114}, + number={3}, + pages={510}, + year={1993}, + publisher={American Psychological Association}, + doi = {10.1037/0033-2909.114.3.510} +} + +@book{mcelreath2020statistical, + title={Statistical rethinking: A Bayesian course with examples in R and Stan}, + author={McElreath, Richard}, + year={2020}, + publisher={CRC press} +} + +@Manual{rcore, + title = {{R}: A Language and Environment for Statistical Computing}, + author = {{R Core Team}}, + organization = {R Foundation for Statistical Computing}, + address = {Vienna, Austria}, + year = {2021}, + url = {https://www.R-project.org/} +} \ No newline at end of file diff --git a/papers/Collabra/paper.Rmd b/papers/Collabra/paper.Rmd new file mode 100644 index 000000000..9f8ae0387 --- /dev/null +++ b/papers/Collabra/paper.Rmd @@ -0,0 +1,311 @@ +--- +title: "Check your outliers! An introduction to identifying statistical outliers in R with *easystats*" +author: + - name: Rémi Thériault + affil: 1,* + orcid: 0000-0003-4315-6788 + - name: Mattan S. Ben-Shachar + affil: 2 + orcid: 0000-0002-4287-4801 + - name: Indrajeet Patil + affil: 3 + orcid: 0000-0003-1995-6531 + - name: Daniel Lüdecke + affil: 4 + orcid: 0000-0002-8895-3206 + - name: Brenton M. Wiernik + affil: 5 + orcid: 0000-0001-9560-6336 + - name: Dominique Makowski + affil: 6 + orcid: 0000-0001-5375-9967 +affiliation: + - num: 1 + address: Department of Psychology, Université du Québec à Montréal, Montréal, Québec, Canada + - num: 2 + address: Independent Researcher + - num: 3 + address: Center for Humans and Machines, Max Planck Institute for Human Development, Berlin, Germany + - num: 4 + address: Institute of Medical Sociology, University Medical Center Hamburg-Eppendorf, Germany + - num: 5 + address: Independent Researcher, Tampa, FL, USA + - num: 6 + address: School of Psychology, University of Sussex, Brighton, UK +correspondence: theriault.remi@courrier.uqam.ca. +journal: "collabra" +type: article +status: submit +bibliography: mybibfile.bib +simplesummary: | + The *{performance}* package from the *easystats* ecosystem makes it easy to + diagnose outliers in R and according to current best practices thanks to the + `check_outiers()` function. +abstract: | + Beyond the challenge of keeping up-to-date with current best practices + regarding the diagnosis and treatment of outliers, an additional difficulty + arises concerning the mathematical implementation of the recommended methods. + In this paper, we provide an overview of current recommandations and best + practices and demonstrate how they can easily and conveniently be + implemented in the R statistical computing software, using the *{performance}* + package of the *easystats* ecosystem. We cover univariate, multivariate, and + model-based statistical outlier detection methods, their recommended + threshold, standard output, and plotting methods. We conclude with + recommendations on the handling of outliers: the different theoretical types + of outliers, whether to exclude or winsorize them, and the importance of + transparency. +keywords: | + univariate outliers; multivariate outliers; robust detection methods; R; easystats +acknowledgement: | + *{performance}* is part of the collaborative + [*easystats*](https://github.com/easystats/easystats) ecosystem + [@easystatspackage]. Thus, we thank all + [members of easystats](https://github.com/orgs/easystats/people), + contributors, and users alike. +authorcontributions: | + R.T. drafted the paper; all authors contributed to both the writing of the + paper and the conception of the software. +funding: | + This research received no external funding. +conflictsofinterest: | + The authors declare no conflict of interest. +abbreviations: + - short: SOD + long: Statistical outlier detection + - short: SEM + long: Structural equation modelling + - short: SD + long: Standard deviation + - short: MAD + long: Median absolute deviation + - short: IQR + long: Interquartile range + - short: HDI + long: Highest density interval + - short: BCI + long: Bias corrected and accelerated interval + - short: MCD + long: Minimum covariance determinant + - short: ICS + long: invariant coordinate selection + - short: OSF + long: Open Science Framework +output: rticles::arxiv_article +--- + +```{r setup, include=FALSE} +knitr::opts_chunk$set( + echo = TRUE, + comment = "#>", + out.width = "100%", + dpi = 300, + warning = FALSE +) + +library(performance) +library(see) +library(datawizard) +``` + +# Introduction + +Real-life data often contain observations that can be considered *abnormal* when compared to the main population. The cause of it---be it because they belong to a different distribution (originating from a different generative process) or simply being extreme cases, statistically rare but not impossible---can be hard to assess, and the boundaries of "abnormal" are hard to define. + +Nonetheless, the improper handling of these outliers can substantially affect statistical model estimations, biasing effect estimations and weakening the models' predictive performance. +It is thus essential to address this problem in a thoughtful manner. Yet, despite the existence of established recommendations and guidelines, many researchers still do not treat outliers in a consistent manner, or do so using inappropriate strategies [@simmons2011false; @leys2013outliers]. + +One possible reason is that researchers are not aware of the existing recommendations, or do not know how to implement them using their analysis software. In this paper, we show how to follow current best practices for automatic and reproducible statistical outlier detection (SOD) using R and the *{performance}* package [@ludecke2021performance], which is part of the *easystats* ecosystem of packages that build an R framework for easy statistical modeling, visualization, and reporting [@easystatspackage]. + +# Identifying Outliers + +Although many researchers attempt to identify outliers with measures based on the mean (e.g., _z_ scores), those methods are problematic because the mean and standard deviation themselves are not robust to the influence of outliers and they assume normally distributed data (i.e., a Gaussian distribution). Therefore, current guidelines recommend using robust methods to identify outliers, such as those relying on the median as opposed to the mean [@leys2019outliers; @leys2013outliers; @leys2018outliers]. + +Nonetheless, which exact outlier method to use depends on many factors. In some cases, eye-gauging odd observations can be an appropriate solution, though many researchers will favour algorithmic solutions to detect potential outliers, for example, based on a continuous value expressing the observation stands out from the others. + +One of the factors to consider when selecting an algorithmic outlier detection method is the statistical test of interest. When using a regression model, relevant information can be found by identifying observations that do not fit well with the model. This approach, known as model-based outliers detection (as outliers are extracted after the statistical model has been fit), can be contrasted with distribution-based outliers detection, which is based on the distance between an observation and the "center" of its population. Various quantification strategies of this distance exist for the latter, both univariate (involving only one variable at a time) or multivariate (involving multiple variables). + +When no method is readily available to detect model-based outliers, such as for structural equation modelling (SEM), looking for multivariate outliers may be of relevance. For simple tests (_t_ tests or correlations) that compare values of the same variable, it can be appropriate to check for univariate outliers. However, univariate methods can give false positives since _t_ tests and correlations, ultimately, are also models/multivariable statistics. They are in this sense more limited, but we show them nonetheless for educational purposes. + +Importantly, whatever approach researchers choose remains a subjective decision, which usage (and rationale) must be transparently documented and reproducible [@leys2019outliers]. Researchers should commit (ideally in a preregistration) to an outlier treatment method before collecting the data. They should report in the paper their decisions and details of their methods, as well as any deviation from their original plan. These transparency practices can help reduce false positives due to excessive researchers' degrees of freedom (i.e., choice flexibility throughout the analysis). In the following section, we will go through each of the mentioned methods and provide examples on how to implement them with R. + +## Univariate Outliers + +Researchers frequently attempt to identify outliers using measures of deviation from the center of a variable's distribution. One of the most popular such procedure is the _z_ score transformation, which computes the distance in standard deviation (SD) from the mean. However, as mentioned earlier, this popular method is not robust. Therefore, for univariate outliers, it is recommended to use the median along with the Median Absolute Deviation (MAD), which are more robust than the interquartile range or the mean and its standard deviation [@leys2019outliers; @leys2013outliers]. + +Researchers can identify outliers based on robust (i.e., MAD-based) _z_ scores using the `check_outliers()` function of the *{performance}* package, by specifying `method = "zscore_robust"`.^[Note that `check_outliers()` only checks numeric variables.] Although @leys2013outliers suggest a default threshold of 2.5 and @leys2019outliers a threshold of 3, *{performance}* uses by default a less conservative threshold of ~3.29.^[3.29 is an approximation of the two-tailed critical value for _p_ < .001, obtained through `qnorm(p = 1 - 0.001 / 2)`. We chose this threshold for consistency with the thresholds of all our other methods.] That is, data points will be flagged as outliers if they go beyond +/- ~3.29 MAD. Users can adjust this threshold using the `threshold` argument, as demonstrated below. + +```{r z_score} +library(performance) + +# Create some artificial outliers and an ID column +data <- rbind(mtcars[1:4], 42, 55) +data <- cbind(car = row.names(data), data) + +outliers <- check_outliers(data, method = "zscore_robust", ID = "car") +outliers +``` + +The row numbers of the detected outliers can be obtained by using `which()` on the output object, which can be used for exclusions for example: + +```{r} +which(outliers) + +data_clean <- data[-which(outliers), ] +``` + +All `check_outliers()` output objects possess a `plot()` method, meaning it is also possible to visualize the outliers: + +```{r univariate, fig.cap = "Visual depiction of outliers using the robust z-score method."} +library(see) + +plot(outliers) +``` + +Other univariate methods are available, such as using the interquartile range (IQR), or based on different intervals, such as the Highest Density Interval (HDI) or the Bias Corrected and Accelerated Interval (BCI). These methods are documented and described in the function's [help page](). + +## Multivariate Outliers + +Univariate outliers can be useful when the focus is on a particular variable, for instance the reaction time, as extreme values might be indicative of inattention or non-task-related behavior^[ Note that they might not be the optimal way of treating reaction time outliers [@ratcliff1993methods; @van1995statistical]]. + +However, in many scenarios, variables of a data set are not independent, and an abnormal observation will impact multiple dimensions. For instance, a participant giving random answers to a questionnaire. In this case, computing the _z_ score for each of the questions might not lead to satisfactory results. Instead, one might want to look at these variables together. + +One common approach for this is to compute multivariate distance metrics such as the Mahalanobis distance. Although the Mahalanobis distance is very popular, just like the regular _z_ scores method, it is not robust and is heavily influenced by the outliers themselves. Therefore, for multivariate outliers, it is recommended to use the Minimum Covariance Determinant, a robust version of the Mahalanobis distance [MCD, @leys2018outliers; @leys2019outliers]. + +In *{performance}*'s `check_outliers()`, one can use this approach with `method = "mcd"`.^[Our default threshold for the MCD method is defined by `stats::qchisq(p = 1 - 0.001, df = ncol(x))`, which again is an approximation of the critical value for _p_ < .001 consistent with the thresholds of our other methods.] + +```{r multivariate, fig.cap = "Visual depiction of outliers using the Minimum Covariance Determinant (MCD) method, a robust version of the Mahalanobis distance."} +outliers <- check_outliers(data, method = "mcd") +outliers + +plot(outliers) +``` + +Other multivariate methods are available, such as another type of robust Mahalanobis distance that in this case relies on an orthogonalized Gnanadesikan-Kettenring pairwise estimator [@gnanadesikan1972robust]. These methods are documented and described in the function's [help page](https://easystats.github.io/performance/reference/check_outliers.html). + +## Model-Based Outliers + +Working with regression models creates the possibility of using model-based SOD methods. These methods rely on the concept of *leverage*, that is, how much influence a given observation can have on the model estimates. If few observations have a relatively strong leverage/influence on the model, one can suspect that the model's estimates are biased by these observations, in which case flagging them as outliers could prove helpful (see next section, "Handling Outliers"). + +In {performance}, two such model-based SOD methods are currently available: Cook's distance, for regular regression models, and Pareto, for Bayesian models. As such, `check_outliers()` can be applied directly on regression model objects, by simply specifying `method = "cook"` (or `method = "pareto"` for Bayesian models).^[Our default threshold for the Cook method is defined by `stats::qf(0.5, ncol(x), nrow(x) - ncol(x))`, which again is an approximation of the critical value for _p_ < .001 consistent with the thresholds of our other methods.] + +```{r model, fig.cap = "Visual depiction of outliers based on Cook's distance (leverage and standardized residuals)."} +model <- lm(disp ~ mpg * disp, data = data) +outliers <- check_outliers(model, method = "cook") +outliers + +plot(outliers) +``` + +Table 1 below summarizes which methods to use in which cases, and with what threshold. + +```{r, echo=FALSE} +df <- data.frame( + `Statistical Test` = c( + "Supported regression model", + "Structural Equation Modeling (or other unsupported model)", + "Simple test with few variables (*t* test, correlation, etc.)"), + `Diagnosis Method` = c( + "**Model-based**: Cook (or Pareto for Bayesian models)", + "**Multivariate**: Minimum Covariance Determinant (MCD)", + "**Univariate**: robust *z* scores (MAD)"), + `Recommended Threshold` = c( + "`qf(0.5, ncol(x), nrow(x) - ncol(x))` (or 0.7 for Pareto)", + "`qchisq(p = 1 - 0.001, df = ncol(x))`", + "`qnorm(p = 1 - 0.001 / 2)`, ~ 3.29") +) +knitr::kable( + df, col.names = gsub("[.]", " ", names(df)), + caption = "Summary of Statistical Outlier Detection Methods Recommendations.", longtable = TRUE) +``` + +### Cook's Distance vs. MCD + +@leys2018outliers report a preference for the MCD method over Cook's distance. This is because Cook's distance removes one observation at a time and checks its corresponding influence on the model each time [@cook1977detection], and flags any observation that has a large influence. In the view of these authors, when there are several outliers, the process of removing a single outlier at a time is problematic as the model remains "contaminated" or influenced by other possible outliers in the model, rendering this method suboptimal in the presence of multiple outliers. + +However, distribution-based approaches are not a silver bullet either, and there are cases where the usage of methods agnostic to theoretical and statistical models of interest might be problematic. For example, a very tall person would be expected to also be much heavier than average, but that would still fit with the expected association between height and weight (i.e., it would be in line with a model such as `weight ~ height`). In contrast, using multivariate outlier detection methods there may flag this person as being an outlier---being unusual on two variables, height and weight---even though the pattern fits perfectly with our predictions. + +In the example below, we plot the raw data and see two possible outliers. The first one falls along the regression line, and is therefore "in line" with our hypothesis. The second one clearly diverges from the regression line, and therefore we can conclude that this outlier may have a disproportionate influence on our model. + +```{r scatter, fig.cap = "Scatter plot of height and weight, with two extreme observations: one model-consistent (top-right) and the other, model-inconsistent (i.e., an outlier; bottom-right)."} +data <- women[rep(seq_len(nrow(women)), each = 100), ] +data <- rbind(data, c(100, 258), c(100, 200)) +model <- lm(weight ~ height, data) +rempsyc::nice_scatter(data, "height", "weight") +``` + +Using either the *z*-score or MCD methods, our model-consistent observation will be incorrectly flagged as an outlier or influential observation. + +```{r} +outliers <- check_outliers(model, method = c("zscore_robust", "mcd")) +which(outliers) +``` + +In contrast, the model-based detection method displays the desired behaviour: it correctly flags the person who is very tall but very light, without flagging the person who is both tall and heavy. + +```{r model2, fig.cap = "The leverage method (Cook's distance) correctly distinguishes the true outlier from the model-consistent extreme observation)."} +outliers <- check_outliers(model, method = "cook") +which(outliers) +plot(outliers) +``` + +Finally, unusual observations happen naturally: extreme observations are expected even when taken from a normal distribution. While statistical models can integrate this "expectation", multivariate outlier methods might be too conservative, flagging too many observations despite belonging to the right generative process. For these reasons, we believe that model-based methods are still preferable to the MCD when using supported regression models. Additionally, if the presence of multiple outliers is a significant concern, regression methods that are more robust to outliers should be considered---like _t_ regression or quantile regression---as they render their precise identification less critical [@mcelreath2020statistical]. + +## Multiple Methods + +An alternative approach that is possible is to combine several methods, based on the assumption that different methods provide different angles of looking at the problem. By applying a variety of methods, one can hope to "triangulate" the true outliers (those consistently flagged by multiple methods) and thus attempt to minimize false positives. + +In practice, this approach computes a composite outlier score, formed of the average of the binary (0 or 1) classification results of each method. It represents the probability that each observation is classified as an outlier by at least one method. The default decision rule classifies rows with composite outlier scores superior or equal to 0.5 as outlier observations (i.e., that were classified as outliers by at least half of the methods). In *{performance}*'s `check_outliers()`, one can use this approach by including all desired methods in the corresponding argument. + +```{r multimethod, fig.cap = "Visual depiction of outliers using several different statistical outlier detection methods."} +outliers <- check_outliers(model, method = c("zscore_robust", "mcd", "cook")) +which(outliers) +``` + +Outliers (counts or per variables) for individual methods can then be obtained through attributes. For example: + +```{r} +attributes(outliers)$outlier_var$zscore_robust +``` + +An example sentence for reporting the usage of the composite method could be: + +> Based on a composite outlier score (see the 'check_outliers()' function in the 'performance' R package, [@ludecke2021performance]) obtained via the joint application of multiple outliers detection algorithms ((a) median absolute deviation (MAD)-based robust _z_ scores, [@leys2013outliers]; (b) Mahalanobis minimum covariance determinant (MCD), [@leys2019outliers]; and (c) Cook's distance, [@cook1977detection]), we excluded two participants that were classified as outliers by at least half of the methods used. + +# Handling Outliers + +The above section demonstrated how to identify outliers using the `check_outliers()` function in the *{performance}* package. But what should we do with these outliers once identified? Although it is common to automatically discard any observation that has been marked as "an outlier" as if it might infect the rest of the data with its statistical ailment, we believe that the use of SOD methods is but one step in the get-to-know-your-data pipeline; a researcher or analyst's _domain knowledge_ must be involved in the decision of how to deal with observations marked as outliers by means of SOD. Indeed, automatic tools can help detect outliers, but they are nowhere near perfect. Although they can be useful to flag suspect data, they can have misses and false alarms, and they cannot replace human eyes and proper vigilance from the researcher. If you do end up manually inspecting your data for outliers, it can be helpful to think of outliers as belonging to different types of outliers, or categories, which can help decide what to do with a given outlier. + +## Error, Interesting, and Random Outliers + +@leys2019outliers distinguish between error outliers, interesting outliers, and random outliers. _Error outliers_ are likely due to human error and should be corrected before data analysis or outright removed since they are invalid observations. _Interesting outliers_ are not due to technical error and may be of theoretical interest; it might thus be relevant to investigate them further even though they should be removed from the current analysis of interest. _Random outliers_ are assumed to be due to chance alone and to belong to the correct distribution and, therefore, should be retained. + +It is recommended to _keep_ observations which are expected to be part of the distribution of interest, even if they are outliers [@leys2019outliers]. However, if it is suspected that the outliers belong to an alternative distribution, then those observations could have a large impact on the results and call into question their robustness, especially if significance is conditional on their inclusion. + +On the other hand, there are also outliers that cannot be detected by statistical tools, but should be found and removed. For example, if we are studying the effects of X on Y among teenagers and we have one observation from a 20-year-old, this observation might not be a _statistical outlier_, but it is an outlier in the _context_ of our research, and should be discarded to allow for valid inferences. + +## Winsorization + +_Removing_ outliers can in this case be a valid strategy, and ideally one would report results with and without outliers to see the extent of their impact on results. This approach however can reduce statistical power. Therefore, some propose a _recoding_ approach, namely, winsorization: bringing outliers back within acceptable limits [e.g., 3 MADs, @tukey1963less]. However, if possible, it is recommended to collect enough data so that even after removing outliers, there is still sufficient statistical power without having to resort to winsorization [@leys2019outliers]. + +The _easystats_ ecosystem makes it easy to incorporate this step into your workflow through the `winsorize()` function of *{datawizard}*, a lightweight R package to facilitate data wrangling and statistical transformations [@patil2022datawizard]. This procedure will bring back univariate outliers within the limits of 'acceptable' values, based either on the percentile, the _z_ score, or its robust alternative based on the MAD. + +```{r winsorization} +data[1501:1502, ] # See outliers rows + +# Winsorizing using the MAD +library(datawizard) +winsorized_data <- winsorize(data, method = "zscore", robust = TRUE, threshold = 3) + +# Values > +/- MAD have been winsorized +winsorized_data[1501:1502, ] +``` + +## The Importance of Transparency + +Once again, it is a critical part of a sound outlier treatment that regardless of which SOD method used, it should be reported in a reproducible manner. Ideally, the handling of outliers should be specified *a priori* with as much detail as possible, and preregistered, to limit researchers' degrees of freedom and therefore risks of false positives [@leys2019outliers]. This is especially true given that interesting outliers and random outliers are often times hard to distinguish in practice. Thus, researchers should always prioritize transparency and report all of the following information: (a) how many outliers were identified; (b) according to which method and criteria, (c) using which function of which R package (if applicable), and (d) how they were handled (excluded or winsorized, if the latter, using what threshold). If at all possible, (e) the corresponding code script along with the data should be shared on a public repository like the Open Science Framework (OSF), so that the exclusion criteria can be reproduced precisely. + +# Conclusion + +In this paper, we have showed how to investigate outliers using the `check_outliers()` function of the *{performance}* package while following current good practices. However, best practice for outlier treatment does not stop at using appropriate statistical algorithms, but entails respecting existing recommendations, such as preregistration, reproducibility, consistency, transparency, and justification. Ideally, one would additionally also report the package, function, and threshold used (linking to the full code when possible). We hope that this paper and the accompanying `check_outlier()` function of *easystats* will help researchers engage in good research practices while providing a smooth outlier detection experience. + +# References \ No newline at end of file diff --git a/papers/Collabra/paper.pdf b/papers/Collabra/paper.pdf new file mode 100644 index 0000000000000000000000000000000000000000..38516cbe1d5f46f14e6e85f16f4d093d7930f0bd GIT binary patch literal 388312 zcma&NW00mnvnJe_wvB1`)10<#+qP|+)3$Bfwr$(C{mpw~cjJpV8?mQ;6tlAG$9-pI zTzMsloRA1LJqZBV%YD9%x4=2V;F}Xt(t!b@haUW+a~+-8`<~a_l(*NS(U{jymmV z?QJ7Qq*n@^(nsEV1I4#GOltHJ9L&b}Gn9pPKl z4zrXoZS*iYjJ0Zuo7m!cFN|Peq#N)q&h4+K>yD5PTOT<(b{ONt(yak|vVJ1ntJq^c zxwq@QtuMyc19er|55Y{bzNQ>-FGYUdsHnNXudVM`NVLuivw*WQyZp{iZhuHU+z!$6NG3ZJdhM~>|g;2j?L%~CYW*Wbnt?@g0gY&=kfd8 z5bIcoP2^WT1MrcBT?miP)VoMBzs5TajkGX1W4B8|IMdU4os|v%xMqN%rE2F6yU@o8D!Ss&*Koas%Kywm^Mx$`BYJg8;}Tj z1bduOPp@)5Xsm=vEIaT@k}xN&ASg)h*xrcy3j8a!#3fs<&e1M+A@pPOcF7>vgMi70 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professional-quality tables +\usepackage{amsfonts} % blackboard math symbols +\usepackage{nicefrac} % compact symbols for 1/2, etc. +\usepackage{microtype} % microtypography +\usepackage{graphicx} + +\title{Check your outliers! An introduction to identifying statistical +outliers in R with \emph{easystats}} + +\author{ + } + +% Pandoc syntax highlighting +\usepackage{color} +\usepackage{fancyvrb} +\newcommand{\VerbBar}{|} +\newcommand{\VERB}{\Verb[commandchars=\\\{\}]} +\DefineVerbatimEnvironment{Highlighting}{Verbatim}{commandchars=\\\{\}} +% Add ',fontsize=\small' for more characters per line +\usepackage{framed} +\definecolor{shadecolor}{RGB}{248,248,248} +\newenvironment{Shaded}{\begin{snugshade}}{\end{snugshade}} +\newcommand{\AlertTok}[1]{\textcolor[rgb]{0.94,0.16,0.16}{#1}} +\newcommand{\AnnotationTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textbf{\textit{#1}}}} +\newcommand{\AttributeTok}[1]{\textcolor[rgb]{0.77,0.63,0.00}{#1}} +\newcommand{\BaseNTok}[1]{\textcolor[rgb]{0.00,0.00,0.81}{#1}} +\newcommand{\BuiltInTok}[1]{#1} +\newcommand{\CharTok}[1]{\textcolor[rgb]{0.31,0.60,0.02}{#1}} +\newcommand{\CommentTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textit{#1}}} +\newcommand{\CommentVarTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textbf{\textit{#1}}}} +\newcommand{\ConstantTok}[1]{\textcolor[rgb]{0.00,0.00,0.00}{#1}} +\newcommand{\ControlFlowTok}[1]{\textcolor[rgb]{0.13,0.29,0.53}{\textbf{#1}}} +\newcommand{\DataTypeTok}[1]{\textcolor[rgb]{0.13,0.29,0.53}{#1}} +\newcommand{\DecValTok}[1]{\textcolor[rgb]{0.00,0.00,0.81}{#1}} +\newcommand{\DocumentationTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textbf{\textit{#1}}}} +\newcommand{\ErrorTok}[1]{\textcolor[rgb]{0.64,0.00,0.00}{\textbf{#1}}} +\newcommand{\ExtensionTok}[1]{#1} +\newcommand{\FloatTok}[1]{\textcolor[rgb]{0.00,0.00,0.81}{#1}} +\newcommand{\FunctionTok}[1]{\textcolor[rgb]{0.00,0.00,0.00}{#1}} +\newcommand{\ImportTok}[1]{#1} +\newcommand{\InformationTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textbf{\textit{#1}}}} +\newcommand{\KeywordTok}[1]{\textcolor[rgb]{0.13,0.29,0.53}{\textbf{#1}}} +\newcommand{\NormalTok}[1]{#1} +\newcommand{\OperatorTok}[1]{\textcolor[rgb]{0.81,0.36,0.00}{\textbf{#1}}} +\newcommand{\OtherTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{#1}} +\newcommand{\PreprocessorTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textit{#1}}} +\newcommand{\RegionMarkerTok}[1]{#1} +\newcommand{\SpecialCharTok}[1]{\textcolor[rgb]{0.00,0.00,0.00}{#1}} +\newcommand{\SpecialStringTok}[1]{\textcolor[rgb]{0.31,0.60,0.02}{#1}} +\newcommand{\StringTok}[1]{\textcolor[rgb]{0.31,0.60,0.02}{#1}} +\newcommand{\VariableTok}[1]{\textcolor[rgb]{0.00,0.00,0.00}{#1}} +\newcommand{\VerbatimStringTok}[1]{\textcolor[rgb]{0.31,0.60,0.02}{#1}} +\newcommand{\WarningTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textbf{\textit{#1}}}} + +% tightlist command for lists without linebreak +\providecommand{\tightlist}{% + \setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}} + +% From pandoc table feature +\usepackage{longtable,booktabs,array} +\usepackage{calc} % for calculating minipage widths +% Correct order of tables after \paragraph or \subparagraph +\usepackage{etoolbox} +\makeatletter +\patchcmd\longtable{\par}{\if@noskipsec\mbox{}\fi\par}{}{} +\makeatother +% Allow footnotes in longtable head/foot +\IfFileExists{footnotehyper.sty}{\usepackage{footnotehyper}}{\usepackage{footnote}} +\makesavenoteenv{longtable} + +% Pandoc citation processing +\newlength{\cslhangindent} +\setlength{\cslhangindent}{1.5em} +\newlength{\csllabelwidth} +\setlength{\csllabelwidth}{3em} +\newlength{\cslentryspacingunit} % times entry-spacing +\setlength{\cslentryspacingunit}{\parskip} +% for Pandoc 2.8 to 2.10.1 +\newenvironment{cslreferences}% + {}% + {\par} +% For Pandoc 2.11+ +\newenvironment{CSLReferences}[2] % #1 hanging-ident, #2 entry spacing + {% don't indent paragraphs + \setlength{\parindent}{0pt} + % turn on hanging indent if param 1 is 1 + \ifodd #1 + \let\oldpar\par + \def\par{\hangindent=\cslhangindent\oldpar} + \fi + % set entry spacing + \setlength{\parskip}{#2\cslentryspacingunit} + }% + {} +\usepackage{calc} +\newcommand{\CSLBlock}[1]{#1\hfill\break} +\newcommand{\CSLLeftMargin}[1]{\parbox[t]{\csllabelwidth}{#1}} +\newcommand{\CSLRightInline}[1]{\parbox[t]{\linewidth - \csllabelwidth}{#1}\break} +\newcommand{\CSLIndent}[1]{\hspace{\cslhangindent}#1} + +\begin{document} +\maketitle + + +\begin{abstract} +Beyond the challenge of keeping up-to-date with current best practices +regarding the diagnosis and treatment of outliers, an additional +difficulty arises concerning the mathematical implementation of the +recommended methods. In this paper, we provide an overview of current +recommandations and best practices and demonstrate how they can easily +and conveniently be implemented in the R statistical computing software, +using the \emph{\{performance\}} package of the \emph{easystats} +ecosystem. We cover univariate, multivariate, and model-based +statistical outlier detection methods, their recommended threshold, +standard output, and plotting methods. We conclude with recommendations +on the handling of outliers: the different theoretical types of +outliers, whether to exclude or winsorize them, and the importance of +transparency. +\end{abstract} + +\keywords{ + univariate outliers; multivariate outliers; robust detection + methods; R; easystats + } + +\hypertarget{introduction}{% +\section{Introduction}\label{introduction}} + +Real-life data often contain observations that can be considered +\emph{abnormal} when compared to the main population. The cause of +it---be it because they belong to a different distribution (originating +from a different generative process) or simply being extreme cases, +statistically rare but not impossible---can be hard to assess, and the +boundaries of ``abnormal'' are hard to define. + +Nonetheless, the improper handling of these outliers can substantially +affect statistical model estimations, biasing effect estimations and +weakening the models' predictive performance. It is thus essential to +address this problem in a thoughtful manner. Yet, despite the existence +of established recommendations and guidelines, many researchers still do +not treat outliers in a consistent manner, or do so using inappropriate +strategies (Simmons, Nelson, and Simonsohn 2011; Leys et al. 2013). + +One possible reason is that researchers are not aware of the existing +recommendations, or do not know how to implement them using their +analysis software. In this paper, we show how to follow current best +practices for automatic and reproducible statistical outlier detection +(SOD) using R and the \emph{\{performance\}} package (Lüdecke et al. +2021), which is part of the \emph{easystats} ecosystem of packages that +build an R framework for easy statistical modeling, visualization, and +reporting (Lüdecke et al. 2022). + +\hypertarget{identifying-outliers}{% +\section{Identifying Outliers}\label{identifying-outliers}} + +Although many researchers attempt to identify outliers with measures +based on the mean (e.g., \emph{z} scores), those methods are problematic +because the mean and standard deviation themselves are not robust to the +influence of outliers and they assume normally distributed data (i.e., a +Gaussian distribution). Therefore, current guidelines recommend using +robust methods to identify outliers, such as those relying on the median +as opposed to the mean (Leys et al. 2019, 2013, 2018). + +Nonetheless, which exact outlier method to use depends on many factors. +In some cases, eye-gauging odd observations can be an appropriate +solution, though many researchers will favour algorithmic solutions to +detect potential outliers, for example, based on a continuous value +expressing the observation stands out from the others. + +One of the factors to consider when selecting an algorithmic outlier +detection method is the statistical test of interest. When using a +regression model, relevant information can be found by identifying +observations that do not fit well with the model. This approach, known +as model-based outliers detection (as outliers are extracted after the +statistical model has been fit), can be contrasted with +distribution-based outliers detection, which is based on the distance +between an observation and the ``center'' of its population. Various +quantification strategies of this distance exist for the latter, both +univariate (involving only one variable at a time) or multivariate +(involving multiple variables). + +When no method is readily available to detect model-based outliers, such +as for structural equation modelling (SEM), looking for multivariate +outliers may be of relevance. For simple tests (\emph{t} tests or +correlations) that compare values of the same variable, it can be +appropriate to check for univariate outliers. However, univariate +methods can give false positives since \emph{t} tests and correlations, +ultimately, are also models/multivariable statistics. They are in this +sense more limited, but we show them nonetheless for educational +purposes. + +Importantly, whatever approach researchers choose remains a subjective +decision, which usage (and rationale) must be transparently documented +and reproducible (Leys et al. 2019). Researchers should commit (ideally +in a preregistration) to an outlier treatment method before collecting +the data. They should report in the paper their decisions and details of +their methods, as well as any deviation from their original plan. These +transparency practices can help reduce false positives due to excessive +researchers' degrees of freedom (i.e., choice flexibility throughout the +analysis). In the following section, we will go through each of the +mentioned methods and provide examples on how to implement them with R. + +\hypertarget{univariate-outliers}{% +\subsection{Univariate Outliers}\label{univariate-outliers}} + +Researchers frequently attempt to identify outliers using measures of +deviation from the center of a variable's distribution. One of the most +popular such procedure is the \emph{z} score transformation, which +computes the distance in standard deviation (SD) from the mean. However, +as mentioned earlier, this popular method is not robust. Therefore, for +univariate outliers, it is recommended to use the median along with the +Median Absolute Deviation (MAD), which are more robust than the +interquartile range or the mean and its standard deviation (Leys et al. +2019, 2013). + +Researchers can identify outliers based on robust (i.e., MAD-based) +\emph{z} scores using the \texttt{check\_outliers()} function of the +\emph{\{performance\}} package, by specifying +\texttt{method\ =\ "zscore\_robust"}.\footnote{Note that + \texttt{check\_outliers()} only checks numeric variables.} Although +Leys et al. (2013) suggest a default threshold of 2.5 and Leys et al. +(2019) a threshold of 3, \emph{\{performance\}} uses by default a less +conservative threshold of \textasciitilde3.29.\footnote{3.29 is an + approximation of the two-tailed critical value for \emph{p} + \textless{} .001, obtained through + \texttt{qnorm(p\ =\ 1\ -\ 0.001\ /\ 2)}. We chose this threshold for + consistency with the thresholds of all our other methods.} That is, +data points will be flagged as outliers if they go beyond +/- +\textasciitilde3.29 MAD. Users can adjust this threshold using the +\texttt{threshold} argument, as demonstrated below. + +\begin{Shaded} +\begin{Highlighting}[] +\FunctionTok{library}\NormalTok{(performance)} + +\CommentTok{\# Create some artificial outliers and an ID column} +\NormalTok{data }\OtherTok{\textless{}{-}} \FunctionTok{rbind}\NormalTok{(mtcars[}\DecValTok{1}\SpecialCharTok{:}\DecValTok{4}\NormalTok{], }\DecValTok{42}\NormalTok{, }\DecValTok{55}\NormalTok{)} +\NormalTok{data }\OtherTok{\textless{}{-}} \FunctionTok{cbind}\NormalTok{(}\AttributeTok{car =} \FunctionTok{row.names}\NormalTok{(data), data)} + +\NormalTok{outliers }\OtherTok{\textless{}{-}} \FunctionTok{check\_outliers}\NormalTok{(data, }\AttributeTok{method =} \StringTok{"zscore\_robust"}\NormalTok{, }\AttributeTok{ID =} \StringTok{"car"}\NormalTok{)} +\NormalTok{outliers} +\end{Highlighting} +\end{Shaded} + +\begin{verbatim} +#> 2 outliers detected: cases 33, 34. +#> - Based on the following method and threshold: zscore_robust (3.291). +#> - For variables: mpg, cyl, disp, hp. +#> +#> ----------------------------------------------------------------------------- +#> +#> The following observations were considered outliers for two or more +#> variables by at least one of the selected methods: +#> +#> Row car n_Zscore_robust +#> 1 33 33 2 +#> 2 34 34 2 +#> +#> ----------------------------------------------------------------------------- +#> Outliers per variable (zscore_robust): +#> +#> $mpg +#> Row car Distance_Zscore_robust +#> 33 33 33 3.709699 +#> 34 34 34 5.848328 +#> +#> $cyl +#> Row car Distance_Zscore_robust +#> 33 33 33 12.14083 +#> 34 34 34 16.52502 +\end{verbatim} + +The row numbers of the detected outliers can be obtained by using +\texttt{which()} on the output object, which can be used for exclusions +for example: + +\begin{Shaded} +\begin{Highlighting}[] +\FunctionTok{which}\NormalTok{(outliers)} +\end{Highlighting} +\end{Shaded} + +\begin{verbatim} +#> [1] 33 34 +\end{verbatim} + +\begin{Shaded} +\begin{Highlighting}[] +\NormalTok{data\_clean }\OtherTok{\textless{}{-}}\NormalTok{ data[}\SpecialCharTok{{-}}\FunctionTok{which}\NormalTok{(outliers), ]} +\end{Highlighting} +\end{Shaded} + +All \texttt{check\_outliers()} output objects possess a \texttt{plot()} +method, meaning it is also possible to visualize the outliers: + +\begin{Shaded} +\begin{Highlighting}[] +\FunctionTok{library}\NormalTok{(see)} + +\FunctionTok{plot}\NormalTok{(outliers)} +\end{Highlighting} +\end{Shaded} + +\begin{figure} +\includegraphics[width=1\linewidth]{paper_files/figure-latex/univariate-1} \caption{Visual depiction of outliers using the robust z-score method.}\label{fig:univariate} +\end{figure} + +Other univariate methods are available, such as using the interquartile +range (IQR), or based on different intervals, such as the Highest +Density Interval (HDI) or the Bias Corrected and Accelerated Interval +(BCI). These methods are documented and described in the function's +\href{https://easystats.github.io/performance/reference/check_outliers.html}{help +page}. + +\hypertarget{multivariate-outliers}{% +\subsection{Multivariate Outliers}\label{multivariate-outliers}} + +Univariate outliers can be useful when the focus is on a particular +variable, for instance the reaction time, as extreme values might be +indicative of inattention or non-task-related behavior\footnote{ Note + that they might not be the optimal way of treating reaction time + outliers (Ratcliff 1993; Van Zandt and Ratcliff 1995)}. + +However, in many scenarios, variables of a data set are not independent, +and an abnormal observation will impact multiple dimensions. For +instance, a participant giving random answers to a questionnaire. In +this case, computing the \emph{z} score for each of the questions might +not lead to satisfactory results. Instead, one might want to look at +these variables together. + +One common approach for this is to compute multivariate distance metrics +such as the Mahalanobis distance. Although the Mahalanobis distance is +very popular, just like the regular \emph{z} scores method, it is not +robust and is heavily influenced by the outliers themselves. Therefore, +for multivariate outliers, it is recommended to use the Minimum +Covariance Determinant, a robust version of the Mahalanobis distance +(MCD, Leys et al. 2018, 2019). + +In \emph{\{performance\}}'s \texttt{check\_outliers()}, one can use this +approach with \texttt{method\ =\ "mcd"}.\footnote{Our default threshold + for the MCD method is defined by + \texttt{stats::qchisq(p\ =\ 1\ -\ 0.001,\ df\ =\ ncol(x))}, which + again is an approximation of the critical value for \emph{p} + \textless{} .001 consistent with the thresholds of our other methods.} + +\begin{Shaded} +\begin{Highlighting}[] +\NormalTok{outliers }\OtherTok{\textless{}{-}} \FunctionTok{check\_outliers}\NormalTok{(data, }\AttributeTok{method =} \StringTok{"mcd"}\NormalTok{)} +\NormalTok{outliers} +\end{Highlighting} +\end{Shaded} + +\begin{verbatim} +#> 9 outliers detected: cases 7, 15, 16, 17, 24, 29, 31, 33, 34. +#> - Based on the following method and threshold: mcd (20). +#> - For variables: mpg, cyl, disp, hp. +\end{verbatim} + +\begin{Shaded} +\begin{Highlighting}[] +\FunctionTok{plot}\NormalTok{(outliers)} +\end{Highlighting} +\end{Shaded} + +\begin{figure} +\includegraphics[width=1\linewidth]{paper_files/figure-latex/multivariate-1} \caption{Visual depiction of outliers using the Minimum Covariance Determinant (MCD) method, a robust version of the Mahalanobis distance.}\label{fig:multivariate} +\end{figure} + +Other multivariate methods are available, such as another type of robust +Mahalanobis distance that in this case relies on an orthogonalized +Gnanadesikan-Kettenring pairwise estimator (Gnanadesikan and Kettenring +1972). These methods are documented and described in the function's +\href{https://easystats.github.io/performance/reference/check_outliers.html}{help +page}. + +\hypertarget{model-based-outliers}{% +\subsection{Model-Based Outliers}\label{model-based-outliers}} + +Working with regression models creates the possibility of using +model-based SOD methods. These methods rely on the concept of +\emph{leverage}, that is, how much influence a given observation can +have on the model estimates. If few observations have a relatively +strong leverage/influence on the model, one can suspect that the model's +estimates are biased by these observations, in which case flagging them +as outliers could prove helpful (see next section, ``Handling +Outliers''). + +In \{performance\}, two such model-based SOD methods are currently +available: Cook's distance, for regular regression models, and Pareto, +for Bayesian models. As such, \texttt{check\_outliers()} can be applied +directly on regression model objects, by simply specifying +\texttt{method\ =\ "cook"} (or \texttt{method\ =\ "pareto"} for Bayesian +models).\footnote{Our default threshold for the Cook method is defined + by \texttt{stats::qf(0.5,\ ncol(x),\ nrow(x)\ -\ ncol(x))}, which + again is an approximation of the critical value for \emph{p} + \textless{} .001 consistent with the thresholds of our other methods.} + +\begin{Shaded} +\begin{Highlighting}[] +\NormalTok{model }\OtherTok{\textless{}{-}} \FunctionTok{lm}\NormalTok{(disp }\SpecialCharTok{\textasciitilde{}}\NormalTok{ mpg }\SpecialCharTok{*}\NormalTok{ disp, }\AttributeTok{data =}\NormalTok{ data)} +\NormalTok{outliers }\OtherTok{\textless{}{-}} \FunctionTok{check\_outliers}\NormalTok{(model, }\AttributeTok{method =} \StringTok{"cook"}\NormalTok{)} +\NormalTok{outliers} +\end{Highlighting} +\end{Shaded} + +\begin{verbatim} +#> 1 outlier detected: case 34. +#> - Based on the following method and threshold: cook (0.708). +#> - For variable: (Whole model). +\end{verbatim} + +\begin{Shaded} +\begin{Highlighting}[] +\FunctionTok{plot}\NormalTok{(outliers)} +\end{Highlighting} +\end{Shaded} + +\begin{figure} +\includegraphics[width=1\linewidth]{paper_files/figure-latex/model-1} \caption{Visual depiction of outliers based on Cook's distance (leverage and standardized residuals).}\label{fig:model} +\end{figure} + +Table 1 below summarizes which methods to use in which cases, and with +what threshold. + +\begin{longtable}[]{@{} + >{\raggedright\arraybackslash}p{(\columnwidth - 4\tabcolsep) * \real{0.3506}} + >{\raggedright\arraybackslash}p{(\columnwidth - 4\tabcolsep) * \real{0.3161}} + >{\raggedright\arraybackslash}p{(\columnwidth - 4\tabcolsep) * \real{0.3333}}@{}} +\caption{Summary of Statistical Outlier Detection Methods +Recommendations.}\tabularnewline +\toprule() +\begin{minipage}[b]{\linewidth}\raggedright +Statistical Test +\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedright +Diagnosis Method +\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedright +Recommended Threshold +\end{minipage} \\ +\midrule() +\endfirsthead +\toprule() +\begin{minipage}[b]{\linewidth}\raggedright +Statistical Test +\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedright +Diagnosis Method +\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedright +Recommended Threshold +\end{minipage} \\ +\midrule() +\endhead +Supported regression model & \textbf{Model-based}: Cook (or Pareto for +Bayesian models) & \texttt{qf(0.5,\ ncol(x),\ nrow(x)\ -\ ncol(x))} (or +0.7 for Pareto) \\ +Structural Equation Modeling (or other unsupported model) & +\textbf{Multivariate}: Minimum Covariance Determinant (MCD) & +\texttt{qchisq(p\ =\ 1\ -\ 0.001,\ df\ =\ ncol(x))} \\ +Simple test with few variables (\emph{t} test, correlation, etc.) & +\textbf{Univariate}: robust \emph{z} scores (MAD) & +\texttt{qnorm(p\ =\ 1\ -\ 0.001\ /\ 2)}, \textasciitilde{} 3.29 \\ +\bottomrule() +\end{longtable} + +\hypertarget{cooks-distance-vs.-mcd}{% +\subsubsection{Cook's Distance vs.~MCD}\label{cooks-distance-vs.-mcd}} + +Leys et al. (2018) report a preference for the MCD method over Cook's +distance. This is because Cook's distance removes one observation at a +time and checks its corresponding influence on the model each time (Cook +1977), and flags any observation that has a large influence. In the view +of these authors, when there are several outliers, the process of +removing a single outlier at a time is problematic as the model remains +``contaminated'' or influenced by other possible outliers in the model, +rendering this method suboptimal in the presence of multiple outliers. + +However, distribution-based approaches are not a silver bullet either, +and there are cases where the usage of methods agnostic to theoretical +and statistical models of interest might be problematic. For example, a +very tall person would be expected to also be much heavier than average, +but that would still fit with the expected association between height +and weight (i.e., it would be in line with a model such as +\texttt{weight\ \textasciitilde{}\ height}). In contrast, using +multivariate outlier detection methods there may flag this person as +being an outlier---being unusual on two variables, height and +weight---even though the pattern fits perfectly with our predictions. + +In the example below, we plot the raw data and see two possible +outliers. The first one falls along the regression line, and is +therefore ``in line'' with our hypothesis. The second one clearly +diverges from the regression line, and therefore we can conclude that +this outlier may have a disproportionate influence on our model. + +\begin{Shaded} +\begin{Highlighting}[] +\NormalTok{data }\OtherTok{\textless{}{-}}\NormalTok{ women[}\FunctionTok{rep}\NormalTok{(}\FunctionTok{seq\_len}\NormalTok{(}\FunctionTok{nrow}\NormalTok{(women)), }\AttributeTok{each =} \DecValTok{100}\NormalTok{), ]} +\NormalTok{data }\OtherTok{\textless{}{-}} \FunctionTok{rbind}\NormalTok{(data, }\FunctionTok{c}\NormalTok{(}\DecValTok{100}\NormalTok{, }\DecValTok{258}\NormalTok{), }\FunctionTok{c}\NormalTok{(}\DecValTok{100}\NormalTok{, }\DecValTok{200}\NormalTok{))} +\NormalTok{model }\OtherTok{\textless{}{-}} \FunctionTok{lm}\NormalTok{(weight }\SpecialCharTok{\textasciitilde{}}\NormalTok{ height, data)} +\NormalTok{rempsyc}\SpecialCharTok{::}\FunctionTok{nice\_scatter}\NormalTok{(data, }\StringTok{"height"}\NormalTok{, }\StringTok{"weight"}\NormalTok{)} +\end{Highlighting} +\end{Shaded} + +\begin{figure} +\includegraphics[width=1\linewidth]{paper_files/figure-latex/scatter-1} \caption{Scatter plot of height and weight, with two extreme observations: one model-consistent (top-right) and the other, model-inconsistent (i.e., an outlier; bottom-right).}\label{fig:scatter} +\end{figure} + +Using either the \emph{z}-score or MCD methods, our model-consistent +observation will be incorrectly flagged as an outlier or influential +observation. + +\begin{Shaded} +\begin{Highlighting}[] +\NormalTok{outliers }\OtherTok{\textless{}{-}} \FunctionTok{check\_outliers}\NormalTok{(model, }\AttributeTok{method =} \FunctionTok{c}\NormalTok{(}\StringTok{"zscore\_robust"}\NormalTok{, }\StringTok{"mcd"}\NormalTok{))} +\FunctionTok{which}\NormalTok{(outliers)} +\end{Highlighting} +\end{Shaded} + +\begin{verbatim} +#> [1] 1501 1502 +\end{verbatim} + +In contrast, the model-based detection method displays the desired +behaviour: it correctly flags the person who is very tall but very +light, without flagging the person who is both tall and heavy. + +\begin{Shaded} +\begin{Highlighting}[] +\NormalTok{outliers }\OtherTok{\textless{}{-}} \FunctionTok{check\_outliers}\NormalTok{(model, }\AttributeTok{method =} \StringTok{"cook"}\NormalTok{)} +\FunctionTok{which}\NormalTok{(outliers)} +\end{Highlighting} +\end{Shaded} + +\begin{verbatim} +#> [1] 1502 +\end{verbatim} + +\begin{Shaded} +\begin{Highlighting}[] +\FunctionTok{plot}\NormalTok{(outliers)} +\end{Highlighting} +\end{Shaded} + +\begin{figure} +\includegraphics[width=1\linewidth]{paper_files/figure-latex/model2-1} \caption{The leverage method (Cook's distance) correctly distinguishes the true outlier from the model-consistent extreme observation).}\label{fig:model2} +\end{figure} + +Finally, unusual observations happen naturally: extreme observations are +expected even when taken from a normal distribution. While statistical +models can integrate this ``expectation'', multivariate outlier methods +might be too conservative, flagging too many observations despite +belonging to the right generative process. For these reasons, we believe +that model-based methods are still preferable to the MCD when using +supported regression models. Additionally, if the presence of multiple +outliers is a significant concern, regression methods that are more +robust to outliers should be considered---like \emph{t} regression or +quantile regression---as they render their precise identification less +critical (McElreath 2020). + +\hypertarget{multiple-methods}{% +\subsection{Multiple Methods}\label{multiple-methods}} + +An alternative approach that is possible is to combine several methods, +based on the assumption that different methods provide different angles +of looking at the problem. By applying a variety of methods, one can +hope to ``triangulate'' the true outliers (those consistently flagged by +multiple methods) and thus attempt to minimize false positives. + +In practice, this approach computes a composite outlier score, formed of +the average of the binary (0 or 1) classification results of each +method. It represents the probability that each observation is +classified as an outlier by at least one method. The default decision +rule classifies rows with composite outlier scores superior or equal to +0.5 as outlier observations (i.e., that were classified as outliers by +at least half of the methods). In \emph{\{performance\}}'s +\texttt{check\_outliers()}, one can use this approach by including all +desired methods in the corresponding argument. + +\begin{Shaded} +\begin{Highlighting}[] +\NormalTok{outliers }\OtherTok{\textless{}{-}} \FunctionTok{check\_outliers}\NormalTok{(model, }\AttributeTok{method =} \FunctionTok{c}\NormalTok{(}\StringTok{"zscore\_robust"}\NormalTok{, }\StringTok{"mcd"}\NormalTok{, }\StringTok{"cook"}\NormalTok{))} +\FunctionTok{which}\NormalTok{(outliers)} +\end{Highlighting} +\end{Shaded} + +\begin{verbatim} +#> [1] 1501 1502 +\end{verbatim} + +Outliers (counts or per variables) for individual methods can then be +obtained through attributes. For example: + +\begin{Shaded} +\begin{Highlighting}[] +\FunctionTok{attributes}\NormalTok{(outliers)}\SpecialCharTok{$}\NormalTok{outlier\_var}\SpecialCharTok{$}\NormalTok{zscore\_robust} +\end{Highlighting} +\end{Shaded} + +\begin{verbatim} +#> $weight +#> Row Distance_Zscore_robust +#> 1501 1501 6.913530 +#> 1502 1502 3.653492 +#> +#> $height +#> Row Distance_Zscore_robust +#> 1501 1501 5.901794 +#> 1502 1502 5.901794 +\end{verbatim} + +An example sentence for reporting the usage of the composite method +could be: + +\begin{quote} +Based on a composite outlier score (see the `check\_outliers()' function +in the `performance' R package, (Lüdecke et al. 2021)) obtained via the +joint application of multiple outliers detection algorithms ((a) median +absolute deviation (MAD)-based robust \emph{z} scores, (Leys et al. +2013); (b) Mahalanobis minimum covariance determinant (MCD), (Leys et +al. 2019); and (c) Cook's distance, (Cook 1977)), we excluded two +participants that were classified as outliers by at least half of the +methods used. +\end{quote} + +\hypertarget{handling-outliers}{% +\section{Handling Outliers}\label{handling-outliers}} + +The above section demonstrated how to identify outliers using the +\texttt{check\_outliers()} function in the \emph{\{performance\}} +package. But what should we do with these outliers once identified? +Although it is common to automatically discard any observation that has +been marked as ``an outlier'' as if it might infect the rest of the data +with its statistical ailment, we believe that the use of SOD methods is +but one step in the get-to-know-your-data pipeline; a researcher or +analyst's \emph{domain knowledge} must be involved in the decision of +how to deal with observations marked as outliers by means of SOD. +Indeed, automatic tools can help detect outliers, but they are nowhere +near perfect. Although they can be useful to flag suspect data, they can +have misses and false alarms, and they cannot replace human eyes and +proper vigilance from the researcher. If you do end up manually +inspecting your data for outliers, it can be helpful to think of +outliers as belonging to different types of outliers, or categories, +which can help decide what to do with a given outlier. + +\hypertarget{error-interesting-and-random-outliers}{% +\subsection{Error, Interesting, and Random +Outliers}\label{error-interesting-and-random-outliers}} + +Leys et al. (2019) distinguish between error outliers, interesting +outliers, and random outliers. \emph{Error outliers} are likely due to +human error and should be corrected before data analysis or outright +removed since they are invalid observations. \emph{Interesting outliers} +are not due to technical error and may be of theoretical interest; it +might thus be relevant to investigate them further even though they +should be removed from the current analysis of interest. \emph{Random +outliers} are assumed to be due to chance alone and to belong to the +correct distribution and, therefore, should be retained. + +It is recommended to \emph{keep} observations which are expected to be +part of the distribution of interest, even if they are outliers (Leys et +al. 2019). However, if it is suspected that the outliers belong to an +alternative distribution, then those observations could have a large +impact on the results and call into question their robustness, +especially if significance is conditional on their inclusion. + +On the other hand, there are also outliers that cannot be detected by +statistical tools, but should be found and removed. For example, if we +are studying the effects of X on Y among teenagers and we have one +observation from a 20-year-old, this observation might not be a +\emph{statistical outlier}, but it is an outlier in the \emph{context} +of our research, and should be discarded to allow for valid inferences. + +\hypertarget{winsorization}{% +\subsection{Winsorization}\label{winsorization}} + +\emph{Removing} outliers can in this case be a valid strategy, and +ideally one would report results with and without outliers to see the +extent of their impact on results. This approach however can reduce +statistical power. Therefore, some propose a \emph{recoding} approach, +namely, winsorization: bringing outliers back within acceptable limits +(e.g., 3 MADs, Tukey and McLaughlin 1963). However, if possible, it is +recommended to collect enough data so that even after removing outliers, +there is still sufficient statistical power without having to resort to +winsorization (Leys et al. 2019). + +The \emph{easystats} ecosystem makes it easy to incorporate this step +into your workflow through the \texttt{winsorize()} function of +\emph{\{datawizard\}}, a lightweight R package to facilitate data +wrangling and statistical transformations (Patil et al. 2022). This +procedure will bring back univariate outliers within the limits of +`acceptable' values, based either on the percentile, the \emph{z} score, +or its robust alternative based on the MAD. + +\begin{Shaded} +\begin{Highlighting}[] +\NormalTok{data[}\DecValTok{1501}\SpecialCharTok{:}\DecValTok{1502}\NormalTok{, ] }\CommentTok{\# See outliers rows} +\end{Highlighting} +\end{Shaded} + +\begin{verbatim} +#> height weight +#> 1501 100 258 +#> 1502 100 200 +\end{verbatim} + +\begin{Shaded} +\begin{Highlighting}[] +\CommentTok{\# Winsorizing using the MAD} +\FunctionTok{library}\NormalTok{(datawizard)} +\NormalTok{winsorized\_data }\OtherTok{\textless{}{-}} \FunctionTok{winsorize}\NormalTok{(data, }\AttributeTok{method =} \StringTok{"zscore"}\NormalTok{, }\AttributeTok{robust =} \ConstantTok{TRUE}\NormalTok{, }\AttributeTok{threshold =} \DecValTok{3}\NormalTok{)} + +\CommentTok{\# Values \textgreater{} +/{-} MAD have been winsorized} +\NormalTok{winsorized\_data[}\DecValTok{1501}\SpecialCharTok{:}\DecValTok{1502}\NormalTok{, ]} +\end{Highlighting} +\end{Shaded} + +\begin{verbatim} +#> height weight +#> 1501 82.7912 188.3736 +#> 1502 82.7912 188.3736 +\end{verbatim} + +\hypertarget{the-importance-of-transparency}{% +\subsection{The Importance of +Transparency}\label{the-importance-of-transparency}} + +Once again, it is a critical part of a sound outlier treatment that +regardless of which SOD method used, it should be reported in a +reproducible manner. Ideally, the handling of outliers should be +specified \emph{a priori} with as much detail as possible, and +preregistered, to limit researchers' degrees of freedom and therefore +risks of false positives (Leys et al. 2019). This is especially true +given that interesting outliers and random outliers are often times hard +to distinguish in practice. Thus, researchers should always prioritize +transparency and report all of the following information: (a) how many +outliers were identified; (b) according to which method and criteria, +(c) using which function of which R package (if applicable), and (d) how +they were handled (excluded or winsorized, if the latter, using what +threshold). If at all possible, (e) the corresponding code script along +with the data should be shared on a public repository like the Open +Science Framework (OSF), so that the exclusion criteria can be +reproduced precisely. + +\hypertarget{conclusion}{% +\section{Conclusion}\label{conclusion}} + +In this paper, we have showed how to investigate outliers using the +\texttt{check\_outliers()} function of the \emph{\{performance\}} +package while following current good practices. However, best practice +for outlier treatment does not stop at using appropriate statistical +algorithms, but entails respecting existing recommendations, such as +preregistration, reproducibility, consistency, transparency, and +justification. Ideally, one would additionally also report the package, +function, and threshold used (linking to the full code when possible). +We hope that this paper and the accompanying \texttt{check\_outlier()} +function of \emph{easystats} will help researchers engage in good +research practices while providing a smooth outlier detection +experience. + +\hypertarget{references}{% +\section*{References}\label{references}} +\addcontentsline{toc}{section}{References} + +\hypertarget{refs}{} +\begin{CSLReferences}{1}{0} +\leavevmode\vadjust pre{\hypertarget{ref-cook1977detection}{}}% +Cook, R. Dennis. 1977. {``Detection of Influential Observation in Linear +Regression.''} \emph{Technometrics} 19 (1): 15--18. +\url{https://doi.org/10.1080/00401706.1977.10489493}. + +\leavevmode\vadjust pre{\hypertarget{ref-gnanadesikan1972robust}{}}% +Gnanadesikan, R., and J. R Kettenring. 1972. {``Robust Estimates, +Residuals, and Outlier Detection with Multiresponse Data.''} +\emph{Biometrics}, 81--124. + +\leavevmode\vadjust pre{\hypertarget{ref-leys2019outliers}{}}% +Leys, Christophe, Marie Delacre, Youri L. Mora, Daniël Lakens, and +Christophe Ley. 2019. {``How to Classify, Detect, and Manage Univariate +and Multivariate Outliers, with Emphasis on Pre-Registration.''} +\emph{International Review of Social Psychology}. +\url{https://doi.org/10.5334/irsp.289}. + +\leavevmode\vadjust pre{\hypertarget{ref-leys2018outliers}{}}% +Leys, Christophe, Olivier Klein, Yves Dominicy, and Christophe Ley. +2018. {``Detecting Multivariate Outliers: Use a Robust Variant of the +Mahalanobis Distance.''} \emph{Journal of Experimental Social +Psychology} 74: 150--56. +\url{https://doi.org/10.1016/j.jesp.2017.09.011}. + +\leavevmode\vadjust pre{\hypertarget{ref-leys2013outliers}{}}% +Leys, Christophe, Christophe Ley, Olivier Klein, Philippe Bernard, and +Laurent Licata. 2013. {``Detecting Outliers: Do Not Use Standard +Deviation Around the Mean, Use Absolute Deviation Around the Median.''} +\emph{Journal of Experimental Social Psychology} 49 (4): 764--66. +\url{https://doi.org/10.1016/j.jesp.2013.03.013}. + +\leavevmode\vadjust pre{\hypertarget{ref-ludecke2021performance}{}}% +Lüdecke, Daniel, Mattan S. Ben-Shachar, Indrajeet Patil, Philip +Waggoner, and Dominique Makowski. 2021. {``{performance}: An r Package +for Assessment, Comparison and Testing of Statistical Models.''} +\emph{Journal of Open Source Software} 6 (60): 3139. +\url{https://doi.org/10.21105/joss.03139}. + +\leavevmode\vadjust pre{\hypertarget{ref-easystatspackage}{}}% +Lüdecke, Daniel, Mattan S. Ben-Shachar, Indrajeet Patil, Brenton M. +Wiernik, Etienne Bacher, Rémi Thériault, and Dominique Makowski. 2022. +{``Easystats: Framework for Easy Statistical Modeling, Visualization, +and Reporting.''} \emph{CRAN}. +\url{https://easystats.github.io/easystats/}. + +\leavevmode\vadjust pre{\hypertarget{ref-mcelreath2020statistical}{}}% +McElreath, Richard. 2020. \emph{Statistical Rethinking: A Bayesian +Course with Examples in r and Stan}. CRC press. + +\leavevmode\vadjust pre{\hypertarget{ref-patil2022datawizard}{}}% +Patil, Indrajeet, Dominique Makowski, Mattan S. Ben-Shachar, Brenton M. +Wiernik, Etienne Bacher, and Daniel Lüdecke. 2022. {``{datawizard}: An +{R} Package for Easy Data Preparation and Statistical +Transformations.''} \emph{Journal of Open Source Software} 7 (78): 4684. +\url{https://doi.org/10.21105/joss.04684}. + +\leavevmode\vadjust pre{\hypertarget{ref-ratcliff1993methods}{}}% +Ratcliff, Roger. 1993. {``Methods for Dealing with Reaction Time +Outliers.''} \emph{Psychological Bulletin} 114 (3): 510. +\url{https://doi.org/10.1037/0033-2909.114.3.510}. + +\leavevmode\vadjust pre{\hypertarget{ref-simmons2011false}{}}% +Simmons, Joseph P., Leif D. Nelson, and Uri Simonsohn. 2011. +{``False-Positive Psychology: Undisclosed Flexibility in Data Collection +and Analysis Allows Presenting Anything as Significant.''} +\emph{Psychological Science} 22 (11): 1359--66. +\url{https://doi.org/10.1177/0956797611417632}. + +\leavevmode\vadjust pre{\hypertarget{ref-tukey1963less}{}}% +Tukey, John W, and Donald H McLaughlin. 1963. {``Less Vulnerable +Confidence and Significance Procedures for Location Based on a Single +Sample: Trimming/Winsorization 1.''} \emph{Sankhy{ā}: The Indian Journal +of Statistics, Series A}, 331--52. + +\leavevmode\vadjust pre{\hypertarget{ref-van1995statistical}{}}% +Van Zandt, Trisha, and Roger Ratcliff. 1995. {``Statistical Mimicking of +Reaction Time Data: Single-Process Models, Parameter Variability, and +Mixtures.''} \emph{Psychonomic Bulletin \& Review} 2 (1): 20--54. +\url{https://doi.org/10.3758/BF03214411}. + +\end{CSLReferences} + +\bibliographystyle{unsrt} +\bibliography{mybibfile.bib} + + +\end{document} diff --git a/papers/Collabra/paper/arxiv.sty b/papers/Collabra/paper/arxiv.sty new file mode 100644 index 000000000..f32d6d899 --- /dev/null +++ b/papers/Collabra/paper/arxiv.sty @@ -0,0 +1,255 @@ +\NeedsTeXFormat{LaTeX2e} + +\ProcessOptions\relax + +% fonts +\renewcommand{\rmdefault}{ptm} +\renewcommand{\sfdefault}{phv} + +% set page geometry +\usepackage[verbose=true,letterpaper]{geometry} +\AtBeginDocument{ + \newgeometry{ + textheight=9in, + textwidth=6.5in, + top=1in, + headheight=14pt, + headsep=25pt, + footskip=30pt + } +} + +\widowpenalty=10000 +\clubpenalty=10000 +\flushbottom +\sloppy + +\usepackage{fancyhdr} +\fancyhf{} +\pagestyle{fancy} +\renewcommand{\headrulewidth}{0pt} +\fancyheadoffset{0pt} +\rhead{\scshape A preprint - \today} +\cfoot{\thepage} + + +%Handling Keywords +\def\keywordname{{\bfseries \emph Keywords}}% +\def\keywords#1{\par\addvspace\medskipamount{\rightskip=0pt plus1cm +\def\and{\ifhmode\unskip\nobreak\fi\ $\cdot$ +}\noindent\keywordname\enspace\ignorespaces#1\par}} + +% font sizes with reduced leading +\renewcommand{\normalsize}{% + \@setfontsize\normalsize\@xpt\@xipt + \abovedisplayskip 7\p@ \@plus 2\p@ \@minus 5\p@ + \abovedisplayshortskip \z@ \@plus 3\p@ + \belowdisplayskip \abovedisplayskip + \belowdisplayshortskip 4\p@ \@plus 3\p@ \@minus 3\p@ +} +\normalsize +\renewcommand{\small}{% + \@setfontsize\small\@ixpt\@xpt + \abovedisplayskip 6\p@ \@plus 1.5\p@ \@minus 4\p@ + \abovedisplayshortskip \z@ \@plus 2\p@ + \belowdisplayskip \abovedisplayskip + \belowdisplayshortskip 3\p@ \@plus 2\p@ \@minus 2\p@ +} +\renewcommand{\footnotesize}{\@setfontsize\footnotesize\@ixpt\@xpt} +\renewcommand{\scriptsize}{\@setfontsize\scriptsize\@viipt\@viiipt} +\renewcommand{\tiny}{\@setfontsize\tiny\@vipt\@viipt} +\renewcommand{\large}{\@setfontsize\large\@xiipt{14}} +\renewcommand{\Large}{\@setfontsize\Large\@xivpt{16}} +\renewcommand{\LARGE}{\@setfontsize\LARGE\@xviipt{20}} +\renewcommand{\huge}{\@setfontsize\huge\@xxpt{23}} +\renewcommand{\Huge}{\@setfontsize\Huge\@xxvpt{28}} + +% sections with less space +\providecommand{\section}{} +\renewcommand{\section}{% + \@startsection{section}{1}{\z@}% + {-2.0ex \@plus -0.5ex \@minus -0.2ex}% + { 1.5ex \@plus 0.3ex \@minus 0.2ex}% + {\large\bf\raggedright}% +} +\providecommand{\subsection}{} +\renewcommand{\subsection}{% + \@startsection{subsection}{2}{\z@}% + {-1.8ex \@plus -0.5ex \@minus -0.2ex}% + { 0.8ex \@plus 0.2ex}% + {\normalsize\bf\raggedright}% +} +\providecommand{\subsubsection}{} +\renewcommand{\subsubsection}{% + \@startsection{subsubsection}{3}{\z@}% + {-1.5ex \@plus -0.5ex \@minus -0.2ex}% + { 0.5ex \@plus 0.2ex}% + {\normalsize\bf\raggedright}% +} +\providecommand{\paragraph}{} +\renewcommand{\paragraph}{% + \@startsection{paragraph}{4}{\z@}% + {1.5ex \@plus 0.5ex \@minus 0.2ex}% + {-1em}% + {\normalsize\bf}% +} +\providecommand{\subparagraph}{} +\renewcommand{\subparagraph}{% + \@startsection{subparagraph}{5}{\z@}% + {1.5ex \@plus 0.5ex \@minus 0.2ex}% + {-1em}% + {\normalsize\bf}% +} +\providecommand{\subsubsubsection}{} +\renewcommand{\subsubsubsection}{% + \vskip5pt{\noindent\normalsize\rm\raggedright}% +} + +% float placement +\renewcommand{\topfraction }{0.85} +\renewcommand{\bottomfraction }{0.4} +\renewcommand{\textfraction }{0.1} +\renewcommand{\floatpagefraction}{0.7} + +\newlength{\@abovecaptionskip}\setlength{\@abovecaptionskip}{7\p@} +\newlength{\@belowcaptionskip}\setlength{\@belowcaptionskip}{\z@} + +\setlength{\abovecaptionskip}{\@abovecaptionskip} +\setlength{\belowcaptionskip}{\@belowcaptionskip} + +% swap above/belowcaptionskip lengths for tables +\renewenvironment{table} + {\setlength{\abovecaptionskip}{\@belowcaptionskip}% + \setlength{\belowcaptionskip}{\@abovecaptionskip}% + \@float{table}} + {\end@float} + +% footnote formatting +\setlength{\footnotesep }{6.65\p@} +\setlength{\skip\footins}{9\p@ \@plus 4\p@ \@minus 2\p@} +\renewcommand{\footnoterule}{\kern-3\p@ \hrule width 12pc \kern 2.6\p@} +\setcounter{footnote}{0} + +% paragraph formatting +\setlength{\parindent}{\z@} +\setlength{\parskip }{5.5\p@} + +% list formatting +\setlength{\topsep }{4\p@ \@plus 1\p@ \@minus 2\p@} +\setlength{\partopsep }{1\p@ \@plus 0.5\p@ \@minus 0.5\p@} +\setlength{\itemsep }{2\p@ \@plus 1\p@ \@minus 0.5\p@} +\setlength{\parsep }{2\p@ \@plus 1\p@ \@minus 0.5\p@} +\setlength{\leftmargin }{3pc} +\setlength{\leftmargini }{\leftmargin} +\setlength{\leftmarginii }{2em} +\setlength{\leftmarginiii}{1.5em} +\setlength{\leftmarginiv }{1.0em} +\setlength{\leftmarginv }{0.5em} +\def\@listi {\leftmargin\leftmargini} +\def\@listii {\leftmargin\leftmarginii + \labelwidth\leftmarginii + \advance\labelwidth-\labelsep + \topsep 2\p@ \@plus 1\p@ \@minus 0.5\p@ + \parsep 1\p@ \@plus 0.5\p@ \@minus 0.5\p@ + \itemsep \parsep} +\def\@listiii{\leftmargin\leftmarginiii + \labelwidth\leftmarginiii + \advance\labelwidth-\labelsep + \topsep 1\p@ \@plus 0.5\p@ \@minus 0.5\p@ + \parsep \z@ + \partopsep 0.5\p@ \@plus 0\p@ \@minus 0.5\p@ + \itemsep \topsep} +\def\@listiv {\leftmargin\leftmarginiv + \labelwidth\leftmarginiv + \advance\labelwidth-\labelsep} +\def\@listv {\leftmargin\leftmarginv + \labelwidth\leftmarginv + \advance\labelwidth-\labelsep} +\def\@listvi {\leftmargin\leftmarginvi + \labelwidth\leftmarginvi + \advance\labelwidth-\labelsep} + +% create title +\providecommand{\maketitle}{} +\renewcommand{\maketitle}{% + \par + \begingroup + \renewcommand{\thefootnote}{\fnsymbol{footnote}} + % for perfect author name centering + \renewcommand{\@makefnmark}{\hbox to \z@{$^{\@thefnmark}$\hss}} + % The footnote-mark was overlapping the footnote-text, + % added the following to fix this problem (MK) + \long\def\@makefntext##1{% + \parindent 1em\noindent + \hbox to 1.8em{\hss $\m@th ^{\@thefnmark}$}##1 + } + \thispagestyle{empty} + \@maketitle + \@thanks + %\@notice + \endgroup + \let\maketitle\relax + \let\thanks\relax +} + +% rules for title box at top of first page +\newcommand{\@toptitlebar}{ + \hrule height 2\p@ + \vskip 0.25in + \vskip -\parskip% +} +\newcommand{\@bottomtitlebar}{ + \vskip 0.29in + \vskip -\parskip + \hrule height 2\p@ + \vskip 0.09in% +} + +% create title (includes both anonymized and non-anonymized versions) +\providecommand{\@maketitle}{} +\renewcommand{\@maketitle}{% + \vbox{% + \hsize\textwidth + \linewidth\hsize + \vskip 0.1in + \@toptitlebar + \centering + {\LARGE\sc \@title\par} + \@bottomtitlebar + \textsc{A Preprint}\\ + \vskip 0.1in + \def\And{% + \end{tabular}\hfil\linebreak[0]\hfil% + \begin{tabular}[t]{c}\bf\rule{\z@}{24\p@}\ignorespaces% + } + \def\AND{% + \end{tabular}\hfil\linebreak[4]\hfil% + \begin{tabular}[t]{c}\bf\rule{\z@}{24\p@}\ignorespaces% + } + \begin{tabular}[t]{c}\bf\rule{\z@}{24\p@}\@author\end{tabular}% + \vskip 0.4in \@minus 0.1in \center{\today} \vskip 0.2in + } +} + +% add conference notice to bottom of first page +\newcommand{\ftype@noticebox}{8} +\newcommand{\@notice}{% + % give a bit of extra room back to authors on first page + \enlargethispage{2\baselineskip}% + \@float{noticebox}[b]% + \footnotesize\@noticestring% + \end@float% +} + +% abstract styling +\renewenvironment{abstract} +{ + \centerline + {\large \bfseries \scshape Abstract} + \begin{quote} +} +{ + \end{quote} +} + +\endinput diff --git a/papers/Collabra/paper/paper.Rmd b/papers/Collabra/paper/paper.Rmd new file mode 100644 index 000000000..ec5f91f14 --- /dev/null +++ b/papers/Collabra/paper/paper.Rmd @@ -0,0 +1,143 @@ +--- +title: A template for the *arxiv* style +authors: + - name: David S. Hippocampus + thanks: Use footnote for providing further information about author (webpage, alternative address)---*not* for acknowledging funding agencies. Optional. + department: Department of Computer Science + affiliation: Cranberry-Lemon University + location: Pittsburgh, PA 15213 + email: hippo@cs.cranberry-lemon.edu + - name: Elias D. Striatum + department: Department of Electrical Engineering + affiliation: Mount-Sheikh University + location: Santa Narimana, Levand + email: stariate@ee.mount-sheikh.edu +abstract: | + Enter the text of your abstract here. +keywords: + - blah + - blee + - bloo + - these are optional and can be removed +bibliography: references.bib +biblio-style: unsrt +output: rticles::arxiv_article +--- + +# Introduction + +Here goes an introduction text + +# Headings: first level +\label{sec:headings} + +You can use directly LaTeX command or Markdown text. + +LaTeX command can be used to reference other section. See Section \ref{sec:headings}. +However, you can also use **bookdown** extensions mechanism for this. + +## Headings: second level + +You can use equation in blocks + +$$ +\xi _{ij}(t)=P(x_{t}=i,x_{t+1}=j|y,v,w;\theta)= {\frac {\alpha _{i}(t)a^{w_t}_{ij}\beta _{j}(t+1)b^{v_{t+1}}_{j}(y_{t+1})}{\sum _{i=1}^{N} \sum _{j=1}^{N} \alpha _{i}(t)a^{w_t}_{ij}\beta _{j}(t+1)b^{v_{t+1}}_{j}(y_{t+1})}} +$$ + +But also inline i.e $z=x+y$ + +### Headings: third level + +Another paragraph. + + +# Examples of citations, figures, tables, references +\label{sec:others} + +You can insert references. Here is some text [@kour2014real; @kour2014fast] and see @hadash2018estimate. + +The documentation for \verb+natbib+ may be found at + +You can use custom blocks with LaTeX support from **rmarkdown** to create environment. + +::: {.center latex=true} + +::: + +Of note is the command \verb+\citet+, which produces citations +appropriate for use in inline text. + +You can insert LaTeX environment directly too. + +\begin{verbatim} + \citet{hasselmo} investigated\dots +\end{verbatim} + +produces + +\begin{quote} + Hasselmo, et al.\ (1995) investigated\dots +\end{quote} + +\begin{center} + \url{https://www.ctan.org/pkg/booktabs} +\end{center} + + +## Figures + +You can insert figure using LaTeX directly. + +See Figure \ref{fig:fig1}. Here is how you add footnotes. [^Sample of the first footnote.] + +\begin{figure} + \centering + \fbox{\rule[-.5cm]{4cm}{4cm} \rule[-.5cm]{4cm}{0cm}} + \caption{Sample figure caption.} + \label{fig:fig1} +\end{figure} + +But you can also do that using R. + +```{r fig2, fig.cap = "Another sample figure"} +plot(mtcars$mpg) +``` + +You can use **bookdown** to allow references for Tables and Figures. + + +## Tables + +Below we can see how to use tables. + +See awesome Table~\ref{tab:table} which is written directly in LaTeX in source Rmd file. + +\begin{table} + \caption{Sample table title} + \centering + \begin{tabular}{lll} + \toprule + \multicolumn{2}{c}{Part} \\ + \cmidrule(r){1-2} + Name & Description & Size ($\mu$m) \\ + \midrule + Dendrite & Input terminal & $\sim$100 \\ + Axon & Output terminal & $\sim$10 \\ + Soma & Cell body & up to $10^6$ \\ + \bottomrule + \end{tabular} + \label{tab:table} +\end{table} + +You can also use R code for that. + +```{r} +knitr::kable(head(mtcars), caption = "Head of mtcars table") +``` + + +## Lists + +- Item 1 +- Item 2 +- Item 3 diff --git a/papers/Collabra/paper/paper.pdf b/papers/Collabra/paper/paper.pdf new file mode 100644 index 0000000000000000000000000000000000000000..0463f855d90bec7ff24af1fc4bc13132ec5658c5 GIT binary patch literal 313449 zcma&MbCf8(vo1Wg%{{hlTYGHVwr%aPZQHhO+qP%E{l4e?*1c<;Z>@X!k93kwI!RR} z_4Lz4A}1_L!$8XdMKZfMvoUN<`U1%k7RYHMvNMNU)0kb2~D8@KJsk-KA+YZh7K4x)Y5_HlEU6GVfVbkgj3U# zh1j|uWfWl&p;uTpzPyy?IZ`wYK?#-I#M;60F|wx0W}5RAJfIg$j>z57HWhXVfli!& zRS>^;k-FOYCV{^5?lF<_=%$fiZpBQk|MZUnB z1aH4;rB8scWy5QAdaK%?E{vXktL z$E;w)Xf2T{ntpCIMo#FLpYsx}PM^+~h@D!a?i0P4bdqx91Mf;~yPI-ssdxpijX)`2 zszhGQgHgy2V}ltl3=-a>H`y;fd@|uUNUp_!lsK|~X=MC>nNk4Wsjg+*u7q}E?!y>W8n+H7%7|51V!b-3edd}EUx zi0|J@eH>6d-hHDI`fTI*>sW^dAjNer8$xpbc+tvHi4ba=C7}@%CWCGTS0m7ds%GAR z!miuVgP?H3gEArY?F^!CEPa~Rgt`45uO{Wj=B~cH|iXud? za6SM8W+!kBECX0x6Es($JWquAV<^x*8jvc)`4t2MtY#5H8F%{KR{4cy!}U%hw>*k{ z*cFL0S0sZEVl9?n|6PJ=ev2$qAY(5!7;7l&r)~eZpB0{tm9?e3T*fY@7=3u=!7RUk 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1/2, etc. +\usepackage{microtype} % microtypography +\usepackage{graphicx} + +\title{A template for the \emph{arxiv} style} + +\author{ + David S. Hippocampus + \thanks{Use footnote for providing further information about author +(webpage, alternative address)---\emph{not} for acknowledging funding +agencies. Optional.} + \\ + Department of Computer Science \\ + Cranberry-Lemon University \\ + Pittsburgh, PA 15213 \\ + \texttt{\href{mailto:hippo@cs.cranberry-lemon.edu}{\nolinkurl{hippo@cs.cranberry-lemon.edu}}} \\ + \And + Elias D. Striatum + \\ + Department of Electrical Engineering \\ + Mount-Sheikh University \\ + Santa Narimana, Levand \\ + \texttt{\href{mailto:stariate@ee.mount-sheikh.edu}{\nolinkurl{stariate@ee.mount-sheikh.edu}}} \\ + } + +% Pandoc syntax highlighting +\usepackage{color} +\usepackage{fancyvrb} +\newcommand{\VerbBar}{|} +\newcommand{\VERB}{\Verb[commandchars=\\\{\}]} +\DefineVerbatimEnvironment{Highlighting}{Verbatim}{commandchars=\\\{\}} +% Add ',fontsize=\small' for more characters per line +\usepackage{framed} +\definecolor{shadecolor}{RGB}{248,248,248} +\newenvironment{Shaded}{\begin{snugshade}}{\end{snugshade}} +\newcommand{\AlertTok}[1]{\textcolor[rgb]{0.94,0.16,0.16}{#1}} +\newcommand{\AnnotationTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textbf{\textit{#1}}}} +\newcommand{\AttributeTok}[1]{\textcolor[rgb]{0.77,0.63,0.00}{#1}} +\newcommand{\BaseNTok}[1]{\textcolor[rgb]{0.00,0.00,0.81}{#1}} +\newcommand{\BuiltInTok}[1]{#1} +\newcommand{\CharTok}[1]{\textcolor[rgb]{0.31,0.60,0.02}{#1}} +\newcommand{\CommentTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textit{#1}}} +\newcommand{\CommentVarTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textbf{\textit{#1}}}} +\newcommand{\ConstantTok}[1]{\textcolor[rgb]{0.00,0.00,0.00}{#1}} +\newcommand{\ControlFlowTok}[1]{\textcolor[rgb]{0.13,0.29,0.53}{\textbf{#1}}} +\newcommand{\DataTypeTok}[1]{\textcolor[rgb]{0.13,0.29,0.53}{#1}} +\newcommand{\DecValTok}[1]{\textcolor[rgb]{0.00,0.00,0.81}{#1}} +\newcommand{\DocumentationTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textbf{\textit{#1}}}} +\newcommand{\ErrorTok}[1]{\textcolor[rgb]{0.64,0.00,0.00}{\textbf{#1}}} +\newcommand{\ExtensionTok}[1]{#1} +\newcommand{\FloatTok}[1]{\textcolor[rgb]{0.00,0.00,0.81}{#1}} +\newcommand{\FunctionTok}[1]{\textcolor[rgb]{0.00,0.00,0.00}{#1}} +\newcommand{\ImportTok}[1]{#1} +\newcommand{\InformationTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textbf{\textit{#1}}}} +\newcommand{\KeywordTok}[1]{\textcolor[rgb]{0.13,0.29,0.53}{\textbf{#1}}} +\newcommand{\NormalTok}[1]{#1} +\newcommand{\OperatorTok}[1]{\textcolor[rgb]{0.81,0.36,0.00}{\textbf{#1}}} +\newcommand{\OtherTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{#1}} +\newcommand{\PreprocessorTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textit{#1}}} +\newcommand{\RegionMarkerTok}[1]{#1} +\newcommand{\SpecialCharTok}[1]{\textcolor[rgb]{0.00,0.00,0.00}{#1}} +\newcommand{\SpecialStringTok}[1]{\textcolor[rgb]{0.31,0.60,0.02}{#1}} +\newcommand{\StringTok}[1]{\textcolor[rgb]{0.31,0.60,0.02}{#1}} +\newcommand{\VariableTok}[1]{\textcolor[rgb]{0.00,0.00,0.00}{#1}} +\newcommand{\VerbatimStringTok}[1]{\textcolor[rgb]{0.31,0.60,0.02}{#1}} +\newcommand{\WarningTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textbf{\textit{#1}}}} + +% tightlist command for lists without linebreak +\providecommand{\tightlist}{% + \setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}} + +% From pandoc table feature +\usepackage{longtable,booktabs,array} +\usepackage{calc} % for calculating minipage widths +% Correct order of tables after \paragraph or \subparagraph +\usepackage{etoolbox} +\makeatletter +\patchcmd\longtable{\par}{\if@noskipsec\mbox{}\fi\par}{}{} +\makeatother +% Allow footnotes in longtable head/foot +\IfFileExists{footnotehyper.sty}{\usepackage{footnotehyper}}{\usepackage{footnote}} +\makesavenoteenv{longtable} + +% Pandoc citation processing +\newlength{\cslhangindent} +\setlength{\cslhangindent}{1.5em} +\newlength{\csllabelwidth} +\setlength{\csllabelwidth}{3em} +\newlength{\cslentryspacingunit} % times entry-spacing +\setlength{\cslentryspacingunit}{\parskip} +% for Pandoc 2.8 to 2.10.1 +\newenvironment{cslreferences}% + {}% + {\par} +% For Pandoc 2.11+ +\newenvironment{CSLReferences}[2] % #1 hanging-ident, #2 entry spacing + {% don't indent paragraphs + \setlength{\parindent}{0pt} + % turn on hanging indent if param 1 is 1 + \ifodd #1 + \let\oldpar\par + \def\par{\hangindent=\cslhangindent\oldpar} + \fi + % set entry spacing + \setlength{\parskip}{#2\cslentryspacingunit} + }% + {} +\usepackage{calc} +\newcommand{\CSLBlock}[1]{#1\hfill\break} +\newcommand{\CSLLeftMargin}[1]{\parbox[t]{\csllabelwidth}{#1}} +\newcommand{\CSLRightInline}[1]{\parbox[t]{\linewidth - \csllabelwidth}{#1}\break} +\newcommand{\CSLIndent}[1]{\hspace{\cslhangindent}#1} + +\begin{document} +\maketitle + + +\begin{abstract} +Enter the text of your abstract here. +\end{abstract} + +\keywords{ + blah + \and + blee + \and + bloo + \and + these are optional and can be removed + } + +\hypertarget{introduction}{% +\section{Introduction}\label{introduction}} + +Here goes an introduction text + +\hypertarget{headings-first-level}{% +\section{Headings: first level}\label{headings-first-level}} + +\label{sec:headings} + +You can use directly LaTeX command or Markdown text. + +LaTeX command can be used to reference other section. See Section +\ref{sec:headings}. However, you can also use \textbf{bookdown} +extensions mechanism for this. + +\hypertarget{headings-second-level}{% +\subsection{Headings: second level}\label{headings-second-level}} + +You can use equation in blocks + +\[ +\xi _{ij}(t)=P(x_{t}=i,x_{t+1}=j|y,v,w;\theta)= {\frac {\alpha _{i}(t)a^{w_t}_{ij}\beta _{j}(t+1)b^{v_{t+1}}_{j}(y_{t+1})}{\sum _{i=1}^{N} \sum _{j=1}^{N} \alpha _{i}(t)a^{w_t}_{ij}\beta _{j}(t+1)b^{v_{t+1}}_{j}(y_{t+1})}} +\] + +But also inline i.e \(z=x+y\) + +\hypertarget{headings-third-level}{% +\subsubsection{Headings: third level}\label{headings-third-level}} + +Another paragraph. + +\hypertarget{examples-of-citations-figures-tables-references}{% +\section{Examples of citations, figures, tables, +references}\label{examples-of-citations-figures-tables-references}} + +\label{sec:others} + +You can insert references. Here is some text (Kour and Saabne 2014b, +2014a) and see Hadash et al. (2018). + +The documentation for \verb+natbib+ may be found at + +You can use custom blocks with LaTeX support from \textbf{rmarkdown} to +create environment. + +\begin{center} +\url{http://mirrors.ctan.org/macros/latex/contrib/natbib/natnotes.pdf\%7D} + +\end{center} + +Of note is the command \verb+\citet+, which produces citations +appropriate for use in inline text. + +You can insert LaTeX environment directly too. + +\begin{verbatim} + \citet{hasselmo} investigated\dots +\end{verbatim} + +produces + +\begin{quote} + Hasselmo, et al.\ (1995) investigated\dots +\end{quote} + +\begin{center} + \url{https://www.ctan.org/pkg/booktabs} +\end{center} + +\hypertarget{figures}{% +\subsection{Figures}\label{figures}} + +You can insert figure using LaTeX directly. + +See Figure \ref{fig:fig1}. Here is how you add footnotes. {[}\^{}Sample +of the first footnote.{]} + +\begin{figure} + \centering + \fbox{\rule[-.5cm]{4cm}{4cm} \rule[-.5cm]{4cm}{0cm}} + \caption{Sample figure caption.} + \label{fig:fig1} +\end{figure} + +But you can also do that using R. + +\begin{Shaded} +\begin{Highlighting}[] +\FunctionTok{plot}\NormalTok{(mtcars}\SpecialCharTok{$}\NormalTok{mpg)} +\end{Highlighting} +\end{Shaded} + +\begin{figure} +\centering +\includegraphics{paper_files/figure-latex/fig2-1.pdf} +\caption{Another sample figure} +\end{figure} + +You can use \textbf{bookdown} to allow references for Tables and +Figures. + +\hypertarget{tables}{% +\subsection{Tables}\label{tables}} + +Below we can see how to use tables. + +See awesome Table\textasciitilde{}\ref{tab:table} which is written +directly in LaTeX in source Rmd file. + +\begin{table} + \caption{Sample table title} + \centering + \begin{tabular}{lll} + \toprule + \multicolumn{2}{c}{Part} \\ + \cmidrule(r){1-2} + Name & Description & Size ($\mu$m) \\ + \midrule + Dendrite & Input terminal & $\sim$100 \\ + Axon & Output terminal & $\sim$10 \\ + Soma & Cell body & up to $10^6$ \\ + \bottomrule + \end{tabular} + \label{tab:table} +\end{table} + +You can also use R code for that. + +\begin{Shaded} +\begin{Highlighting}[] +\NormalTok{knitr}\SpecialCharTok{::}\FunctionTok{kable}\NormalTok{(}\FunctionTok{head}\NormalTok{(mtcars), }\AttributeTok{caption =} \StringTok{"Head of mtcars table"}\NormalTok{)} +\end{Highlighting} +\end{Shaded} + +\begin{longtable}[]{@{} + >{\raggedright\arraybackslash}p{(\columnwidth - 22\tabcolsep) * \real{0.2609}} + >{\raggedleft\arraybackslash}p{(\columnwidth - 22\tabcolsep) * \real{0.0725}} + >{\raggedleft\arraybackslash}p{(\columnwidth - 22\tabcolsep) * \real{0.0580}} + >{\raggedleft\arraybackslash}p{(\columnwidth - 22\tabcolsep) * \real{0.0725}} + >{\raggedleft\arraybackslash}p{(\columnwidth - 22\tabcolsep) * \real{0.0580}} + >{\raggedleft\arraybackslash}p{(\columnwidth - 22\tabcolsep) * \real{0.0725}} + >{\raggedleft\arraybackslash}p{(\columnwidth - 22\tabcolsep) * \real{0.0870}} + >{\raggedleft\arraybackslash}p{(\columnwidth - 22\tabcolsep) * \real{0.0870}} + >{\raggedleft\arraybackslash}p{(\columnwidth - 22\tabcolsep) * \real{0.0435}} + >{\raggedleft\arraybackslash}p{(\columnwidth - 22\tabcolsep) * \real{0.0435}} + >{\raggedleft\arraybackslash}p{(\columnwidth - 22\tabcolsep) * \real{0.0725}} + >{\raggedleft\arraybackslash}p{(\columnwidth - 22\tabcolsep) * \real{0.0725}}@{}} +\caption{Head of mtcars table}\tabularnewline +\toprule() +\begin{minipage}[b]{\linewidth}\raggedright +\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft +mpg +\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft +cyl +\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft +disp +\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft +hp +\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft +drat +\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft +wt +\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft +qsec +\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft +vs +\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft +am +\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft +gear +\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft +carb +\end{minipage} \\ +\midrule() +\endfirsthead +\toprule() +\begin{minipage}[b]{\linewidth}\raggedright +\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft +mpg +\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft +cyl +\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft +disp +\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft +hp +\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft +drat +\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft +wt +\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft +qsec +\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft +vs +\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft +am +\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft +gear +\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft +carb +\end{minipage} \\ +\midrule() +\endhead +Mazda RX4 & 21.0 & 6 & 160 & 110 & 3.90 & 2.620 & 16.46 & 0 & 1 & 4 & +4 \\ +Mazda RX4 Wag & 21.0 & 6 & 160 & 110 & 3.90 & 2.875 & 17.02 & 0 & 1 & 4 +& 4 \\ +Datsun 710 & 22.8 & 4 & 108 & 93 & 3.85 & 2.320 & 18.61 & 1 & 1 & 4 & +1 \\ +Hornet 4 Drive & 21.4 & 6 & 258 & 110 & 3.08 & 3.215 & 19.44 & 1 & 0 & 3 +& 1 \\ +Hornet Sportabout & 18.7 & 8 & 360 & 175 & 3.15 & 3.440 & 17.02 & 0 & 0 +& 3 & 2 \\ +Valiant & 18.1 & 6 & 225 & 105 & 2.76 & 3.460 & 20.22 & 1 & 0 & 3 & 1 \\ +\bottomrule() +\end{longtable} + +\hypertarget{lists}{% +\subsection{Lists}\label{lists}} + +\begin{itemize} +\tightlist +\item + Item 1 +\item + Item 2 +\item + Item 3 +\end{itemize} + +\hypertarget{refs}{} +\begin{CSLReferences}{1}{0} +\leavevmode\vadjust pre{\hypertarget{ref-hadash2018estimate}{}}% +Hadash, Guy, Einat Kermany, Boaz Carmeli, Ofer Lavi, George Kour, and +Alon Jacovi. 2018. {``Estimate and Replace: A Novel Approach to +Integrating Deep Neural Networks with Existing Applications.''} +\emph{arXiv Preprint arXiv:1804.09028}. + +\leavevmode\vadjust pre{\hypertarget{ref-kour2014fast}{}}% +Kour, George, and Raid Saabne. 2014a. {``Fast Classification of +Handwritten on-Line Arabic Characters.''} In \emph{Soft Computing and +Pattern Recognition (SoCPaR), 2014 6th International Conference of}, +312--18. IEEE. + +\leavevmode\vadjust pre{\hypertarget{ref-kour2014real}{}}% +---------. 2014b. {``Real-Time Segmentation of on-Line Handwritten +Arabic Script.''} In \emph{Frontiers in Handwriting Recognition (ICFHR), +2014 14th International Conference on}, 417--22. IEEE. + +\end{CSLReferences} + +\bibliographystyle{unsrt} +\bibliography{references.bib} + + +\end{document} diff --git a/papers/Collabra/paper/paper_files/figure-latex/fig2-1.pdf b/papers/Collabra/paper/paper_files/figure-latex/fig2-1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..b793fa72fcc4e75c51dd050fd513a1356e196025 GIT binary patch literal 6205 zcmZ{ocOYC__xB~PxCnya>O<5phEYdN^b%2{jyeVtW(G5QFF_0vq6E=fLPU>FBua$Q zqlbhby67$O8}7}0?(^LDJ^!7x*V=3Cwf8yabG|%!Dr!JcVR3Svkhzfgkp7Tis5`kR zKm>rcyH74BM-EbUhudNiXq1XA77pN7kpYW<#YDtKz@lOz(qiHQU0o-ECc+5HJit*8}V7fhC0LxufkpU~u>IQE_3gFqmMw$b~*P36Lu&ki${-=T(6J zt_A=y@^OU&K+3jQTNkt=0HkN@2*&`#2o45-{{%?=E8yJk+}j;cXGam3?8 zCGZIl_&okWK-(i__C6;KO%NLWx~X|qVP*!!QL8XC^SY{V^tG?mvXBKkWUuna?)?7x z{+IoaMXje_R@c+LYUS5YT1wAaPZs-gld*Ij%8?hqL5_M zi+C^WowdwYJg+sk98ieGdIhZG@e z_G7MTt4d++t_J%G{FH<#UEC)_3%m62@m?KSADYH(2jGH+^66?4RSV;NZl&Z%gI9^^ zs?WC#)ntmblgkzpG2_mf9(Dqp=h+{8B)0Hl7L(*Qikn998QO4oS257kNq2^rKku$o 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zfVUgWo=gx37AC`H{__Hgiiik_0PTT)*&tZ8fxCc+ziePpY^wjXVLxnOb;5tyz+h|_ z{>ugt``3O#LV{Rv^q+o$5Zw9y+a~cZn}~$OzjBBQO8l!nQLqG7QvK(Cq7b2f$3n!h z-z Date: Sun, 2 Apr 2023 15:59:54 -0400 Subject: [PATCH 02/34] address reviewer comment on x labels with ggplot layers [skip ci] --- papers/Collabra/paper.Rmd | 26 +++++++++++++++--- papers/Collabra/paper.pdf | Bin 388312 -> 388564 bytes papers/Collabra/paper.tex | 8 +++--- .../paper_files/figure-latex/model-1.pdf | Bin 7823 -> 7820 bytes .../paper_files/figure-latex/model2-1.pdf | Bin 8534 -> 8531 bytes .../figure-latex/multivariate-1.pdf | Bin 5096 -> 5096 bytes .../figure-latex/multivariate_implicit-1.pdf | Bin 0 -> 5104 bytes .../paper_files/figure-latex/scatter-1.pdf | Bin 7724 -> 7724 bytes .../figure-latex/univariate_implicit-1.pdf | Bin 0 -> 5117 bytes 9 files changed, 26 insertions(+), 8 deletions(-) create mode 100644 papers/Collabra/paper_files/figure-latex/multivariate_implicit-1.pdf create mode 100644 papers/Collabra/paper_files/figure-latex/univariate_implicit-1.pdf diff --git a/papers/Collabra/paper.Rmd b/papers/Collabra/paper.Rmd index 9f8ae0387..2d20786b3 100644 --- a/papers/Collabra/paper.Rmd +++ b/papers/Collabra/paper.Rmd @@ -155,12 +155,21 @@ data_clean <- data[-which(outliers), ] All `check_outliers()` output objects possess a `plot()` method, meaning it is also possible to visualize the outliers: -```{r univariate, fig.cap = "Visual depiction of outliers using the robust z-score method."} +```{r univariate, eval=FALSE} library(see) plot(outliers) ``` +```{r univariate_implicit, fig.cap = "Visual depiction of outliers using the robust z-score method. The distance represents an aggregate score for variables mpg, cyl, disp, and hp.", echo=FALSE} +library(see) + +plot(outliers) + + ggplot2::theme(axis.text.x = ggplot2::element_text( + angle = 45, size = 7 +)) +``` + Other univariate methods are available, such as using the interquartile range (IQR), or based on different intervals, such as the Highest Density Interval (HDI) or the Bias Corrected and Accelerated Interval (BCI). These methods are documented and described in the function's [help page](). ## Multivariate Outliers @@ -173,13 +182,22 @@ One common approach for this is to compute multivariate distance metrics such as In *{performance}*'s `check_outliers()`, one can use this approach with `method = "mcd"`.^[Our default threshold for the MCD method is defined by `stats::qchisq(p = 1 - 0.001, df = ncol(x))`, which again is an approximation of the critical value for _p_ < .001 consistent with the thresholds of our other methods.] -```{r multivariate, fig.cap = "Visual depiction of outliers using the Minimum Covariance Determinant (MCD) method, a robust version of the Mahalanobis distance."} +```{r multivariate} outliers <- check_outliers(data, method = "mcd") outliers +``` +```{r multivariate_plot, eval=FALSE} plot(outliers) ``` +```{r multivariate_implicit, fig.cap = "Visual depiction of outliers using the Minimum Covariance Determinant (MCD) method, a robust version of the Mahalanobis distance. The distance represents the MCD scores for variables mpg, cyl, disp, and hp.", echo=FALSE} +plot(outliers) + + ggplot2::theme(axis.text.x = ggplot2::element_text( + angle = 45, size = 7 +)) +``` + Other multivariate methods are available, such as another type of robust Mahalanobis distance that in this case relies on an orthogonalized Gnanadesikan-Kettenring pairwise estimator [@gnanadesikan1972robust]. These methods are documented and described in the function's [help page](https://easystats.github.io/performance/reference/check_outliers.html). ## Model-Based Outliers @@ -188,7 +206,7 @@ Working with regression models creates the possibility of using model-based SOD In {performance}, two such model-based SOD methods are currently available: Cook's distance, for regular regression models, and Pareto, for Bayesian models. As such, `check_outliers()` can be applied directly on regression model objects, by simply specifying `method = "cook"` (or `method = "pareto"` for Bayesian models).^[Our default threshold for the Cook method is defined by `stats::qf(0.5, ncol(x), nrow(x) - ncol(x))`, which again is an approximation of the critical value for _p_ < .001 consistent with the thresholds of our other methods.] -```{r model, fig.cap = "Visual depiction of outliers based on Cook's distance (leverage and standardized residuals)."} +```{r model, fig.cap = "Visual depiction of outliers based on Cook's distance (leverage and standardized residuals), based on the fitted model."} model <- lm(disp ~ mpg * disp, data = data) outliers <- check_outliers(model, method = "cook") outliers @@ -242,7 +260,7 @@ which(outliers) In contrast, the model-based detection method displays the desired behaviour: it correctly flags the person who is very tall but very light, without flagging the person who is both tall and heavy. 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robust z-score method.}\label{fig:univariate} +\includegraphics[width=1\linewidth]{paper_files/figure-latex/univariate_implicit-1} \caption{Visual depiction of outliers using the robust z-score method. The distance represents an aggregate score for variables mpg, cyl, disp, and hp.}\label{fig:univariate_implicit} \end{figure} Other univariate methods are available, such as using the interquartile @@ -372,7 +372,7 @@ \subsection{Multivariate Outliers}\label{multivariate-outliers}} \end{Shaded} \begin{figure} -\includegraphics[width=1\linewidth]{paper_files/figure-latex/multivariate-1} \caption{Visual depiction of outliers using the Minimum Covariance Determinant (MCD) method, a robust version of the Mahalanobis distance.}\label{fig:multivariate} +\includegraphics[width=1\linewidth]{paper_files/figure-latex/multivariate_implicit-1} \caption{Visual depiction of outliers using the Minimum Covariance Determinant (MCD) method, a robust version of the Mahalanobis distance. The distance represents the MCD scores for variables mpg, cyl, disp, and hp.}\label{fig:multivariate_implicit} \end{figure} Other multivariate methods are available, such as another type of robust @@ -425,7 +425,7 @@ \subsection{Model-Based Outliers}\label{model-based-outliers}} \end{Shaded} \begin{figure} -\includegraphics[width=1\linewidth]{paper_files/figure-latex/model-1} \caption{Visual depiction of outliers based on Cook's distance (leverage and standardized residuals).}\label{fig:model} +\includegraphics[width=1\linewidth]{paper_files/figure-latex/model-1} \caption{Visual depiction of outliers based on Cook's distance (leverage and standardized residuals), based on the fitted model.}\label{fig:model} \end{figure} Table 1 below summarizes which methods to use in which cases, and with @@ -548,7 +548,7 @@ \subsubsection{Cook's Distance vs.~MCD}\label{cooks-distance-vs.-mcd}} \end{Shaded} \begin{figure} -\includegraphics[width=1\linewidth]{paper_files/figure-latex/model2-1} 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03/34] remove test template files [skip ci] --- papers/Collabra/paper.Rmd | 2 +- papers/Collabra/paper/arxiv.sty | 255 ----------- papers/Collabra/paper/paper.Rmd | 143 ------- papers/Collabra/paper/paper.pdf | Bin 313449 -> 0 bytes papers/Collabra/paper/paper.tex | 398 ------------------ .../paper/paper_files/figure-latex/fig2-1.pdf | Bin 6205 -> 0 bytes papers/Collabra/paper/references.bib | 24 -- 7 files changed, 1 insertion(+), 821 deletions(-) delete mode 100644 papers/Collabra/paper/arxiv.sty delete mode 100644 papers/Collabra/paper/paper.Rmd delete mode 100644 papers/Collabra/paper/paper.pdf delete mode 100644 papers/Collabra/paper/paper.tex delete mode 100644 papers/Collabra/paper/paper_files/figure-latex/fig2-1.pdf delete mode 100644 papers/Collabra/paper/references.bib diff --git a/papers/Collabra/paper.Rmd b/papers/Collabra/paper.Rmd index 2d20786b3..4208cb67a 100644 --- a/papers/Collabra/paper.Rmd +++ b/papers/Collabra/paper.Rmd @@ -45,7 +45,7 @@ abstract: | Beyond the challenge of keeping up-to-date with current best practices regarding the diagnosis and treatment of outliers, an additional difficulty arises concerning the mathematical implementation of the recommended methods. - In this paper, we provide an overview of current recommandations and best + In this paper, we provide an overview of current recommendations and best practices and demonstrate how they can easily and conveniently be implemented in the R statistical computing software, using the *{performance}* package of the *easystats* ecosystem. We cover univariate, multivariate, and diff --git a/papers/Collabra/paper/arxiv.sty b/papers/Collabra/paper/arxiv.sty deleted file mode 100644 index f32d6d899..000000000 --- a/papers/Collabra/paper/arxiv.sty +++ /dev/null @@ -1,255 +0,0 @@ -\NeedsTeXFormat{LaTeX2e} - -\ProcessOptions\relax - -% fonts -\renewcommand{\rmdefault}{ptm} -\renewcommand{\sfdefault}{phv} - -% set page geometry -\usepackage[verbose=true,letterpaper]{geometry} -\AtBeginDocument{ - \newgeometry{ - textheight=9in, - textwidth=6.5in, - top=1in, - headheight=14pt, - headsep=25pt, - footskip=30pt - } -} - -\widowpenalty=10000 -\clubpenalty=10000 -\flushbottom -\sloppy - -\usepackage{fancyhdr} -\fancyhf{} -\pagestyle{fancy} -\renewcommand{\headrulewidth}{0pt} -\fancyheadoffset{0pt} -\rhead{\scshape A preprint - \today} -\cfoot{\thepage} - - -%Handling Keywords -\def\keywordname{{\bfseries \emph Keywords}}% -\def\keywords#1{\par\addvspace\medskipamount{\rightskip=0pt plus1cm -\def\and{\ifhmode\unskip\nobreak\fi\ $\cdot$ -}\noindent\keywordname\enspace\ignorespaces#1\par}} - -% font sizes with reduced leading -\renewcommand{\normalsize}{% - \@setfontsize\normalsize\@xpt\@xipt - \abovedisplayskip 7\p@ \@plus 2\p@ \@minus 5\p@ - \abovedisplayshortskip \z@ \@plus 3\p@ - \belowdisplayskip \abovedisplayskip - \belowdisplayshortskip 4\p@ \@plus 3\p@ \@minus 3\p@ -} -\normalsize -\renewcommand{\small}{% - \@setfontsize\small\@ixpt\@xpt - \abovedisplayskip 6\p@ \@plus 1.5\p@ \@minus 4\p@ - \abovedisplayshortskip \z@ \@plus 2\p@ - \belowdisplayskip \abovedisplayskip - \belowdisplayshortskip 3\p@ \@plus 2\p@ \@minus 2\p@ -} -\renewcommand{\footnotesize}{\@setfontsize\footnotesize\@ixpt\@xpt} -\renewcommand{\scriptsize}{\@setfontsize\scriptsize\@viipt\@viiipt} -\renewcommand{\tiny}{\@setfontsize\tiny\@vipt\@viipt} -\renewcommand{\large}{\@setfontsize\large\@xiipt{14}} -\renewcommand{\Large}{\@setfontsize\Large\@xivpt{16}} -\renewcommand{\LARGE}{\@setfontsize\LARGE\@xviipt{20}} -\renewcommand{\huge}{\@setfontsize\huge\@xxpt{23}} -\renewcommand{\Huge}{\@setfontsize\Huge\@xxvpt{28}} - -% sections with less space -\providecommand{\section}{} -\renewcommand{\section}{% - \@startsection{section}{1}{\z@}% - {-2.0ex \@plus -0.5ex \@minus -0.2ex}% - { 1.5ex \@plus 0.3ex \@minus 0.2ex}% - {\large\bf\raggedright}% -} -\providecommand{\subsection}{} -\renewcommand{\subsection}{% - \@startsection{subsection}{2}{\z@}% - {-1.8ex \@plus -0.5ex \@minus -0.2ex}% - { 0.8ex \@plus 0.2ex}% - {\normalsize\bf\raggedright}% -} -\providecommand{\subsubsection}{} -\renewcommand{\subsubsection}{% - \@startsection{subsubsection}{3}{\z@}% - {-1.5ex \@plus -0.5ex \@minus -0.2ex}% - { 0.5ex \@plus 0.2ex}% - {\normalsize\bf\raggedright}% -} -\providecommand{\paragraph}{} -\renewcommand{\paragraph}{% - \@startsection{paragraph}{4}{\z@}% - {1.5ex \@plus 0.5ex \@minus 0.2ex}% - {-1em}% - {\normalsize\bf}% -} -\providecommand{\subparagraph}{} -\renewcommand{\subparagraph}{% - \@startsection{subparagraph}{5}{\z@}% - {1.5ex \@plus 0.5ex \@minus 0.2ex}% - {-1em}% - {\normalsize\bf}% -} -\providecommand{\subsubsubsection}{} -\renewcommand{\subsubsubsection}{% - 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\labelwidth\leftmarginii - \advance\labelwidth-\labelsep - \topsep 2\p@ \@plus 1\p@ \@minus 0.5\p@ - \parsep 1\p@ \@plus 0.5\p@ \@minus 0.5\p@ - \itemsep \parsep} -\def\@listiii{\leftmargin\leftmarginiii - \labelwidth\leftmarginiii - \advance\labelwidth-\labelsep - \topsep 1\p@ \@plus 0.5\p@ \@minus 0.5\p@ - \parsep \z@ - \partopsep 0.5\p@ \@plus 0\p@ \@minus 0.5\p@ - \itemsep \topsep} -\def\@listiv {\leftmargin\leftmarginiv - \labelwidth\leftmarginiv - \advance\labelwidth-\labelsep} -\def\@listv {\leftmargin\leftmarginv - \labelwidth\leftmarginv - \advance\labelwidth-\labelsep} -\def\@listvi {\leftmargin\leftmarginvi - \labelwidth\leftmarginvi - \advance\labelwidth-\labelsep} - -% create title -\providecommand{\maketitle}{} -\renewcommand{\maketitle}{% - \par - \begingroup - \renewcommand{\thefootnote}{\fnsymbol{footnote}} - % for perfect author name centering - \renewcommand{\@makefnmark}{\hbox to \z@{$^{\@thefnmark}$\hss}} - % The footnote-mark was overlapping the footnote-text, - % added the following to fix this problem (MK) - \long\def\@makefntext##1{% - \parindent 1em\noindent - \hbox to 1.8em{\hss $\m@th ^{\@thefnmark}$}##1 - } - \thispagestyle{empty} - \@maketitle - \@thanks - %\@notice - \endgroup - \let\maketitle\relax - \let\thanks\relax -} - -% rules for title box at top of first page -\newcommand{\@toptitlebar}{ - \hrule height 2\p@ - \vskip 0.25in - \vskip -\parskip% -} -\newcommand{\@bottomtitlebar}{ - \vskip 0.29in - \vskip -\parskip - \hrule height 2\p@ - \vskip 0.09in% -} - -% create title (includes both anonymized and non-anonymized versions) -\providecommand{\@maketitle}{} -\renewcommand{\@maketitle}{% - \vbox{% - \hsize\textwidth - \linewidth\hsize - \vskip 0.1in - \@toptitlebar - \centering - {\LARGE\sc \@title\par} - \@bottomtitlebar - \textsc{A Preprint}\\ - \vskip 0.1in - \def\And{% - \end{tabular}\hfil\linebreak[0]\hfil% - \begin{tabular}[t]{c}\bf\rule{\z@}{24\p@}\ignorespaces% - } - \def\AND{% - \end{tabular}\hfil\linebreak[4]\hfil% - \begin{tabular}[t]{c}\bf\rule{\z@}{24\p@}\ignorespaces% - } - \begin{tabular}[t]{c}\bf\rule{\z@}{24\p@}\@author\end{tabular}% - \vskip 0.4in \@minus 0.1in \center{\today} \vskip 0.2in - } -} - -% add conference notice to bottom of first page -\newcommand{\ftype@noticebox}{8} -\newcommand{\@notice}{% - % give a bit of extra room back to authors on first page - \enlargethispage{2\baselineskip}% - \@float{noticebox}[b]% - \footnotesize\@noticestring% - \end@float% -} - -% abstract styling -\renewenvironment{abstract} -{ - \centerline - {\large \bfseries \scshape Abstract} - \begin{quote} -} -{ - \end{quote} -} - -\endinput diff --git a/papers/Collabra/paper/paper.Rmd b/papers/Collabra/paper/paper.Rmd deleted file mode 100644 index ec5f91f14..000000000 --- a/papers/Collabra/paper/paper.Rmd +++ /dev/null @@ -1,143 +0,0 @@ ---- -title: A template for the *arxiv* style -authors: - - name: David S. Hippocampus - thanks: Use footnote for providing further information about author (webpage, alternative address)---*not* for acknowledging funding agencies. Optional. - department: Department of Computer Science - affiliation: Cranberry-Lemon University - location: Pittsburgh, PA 15213 - email: hippo@cs.cranberry-lemon.edu - - name: Elias D. Striatum - department: Department of Electrical Engineering - affiliation: Mount-Sheikh University - location: Santa Narimana, Levand - email: stariate@ee.mount-sheikh.edu -abstract: | - Enter the text of your abstract here. -keywords: - - blah - - blee - - bloo - - these are optional and can be removed -bibliography: references.bib -biblio-style: unsrt -output: rticles::arxiv_article ---- - -# Introduction - -Here goes an introduction text - -# Headings: first level -\label{sec:headings} - -You can use directly LaTeX command or Markdown text. - -LaTeX command can be used to reference other section. See Section \ref{sec:headings}. -However, you can also use **bookdown** extensions mechanism for this. - -## Headings: second level - -You can use equation in blocks - -$$ -\xi _{ij}(t)=P(x_{t}=i,x_{t+1}=j|y,v,w;\theta)= {\frac {\alpha _{i}(t)a^{w_t}_{ij}\beta _{j}(t+1)b^{v_{t+1}}_{j}(y_{t+1})}{\sum _{i=1}^{N} \sum _{j=1}^{N} \alpha _{i}(t)a^{w_t}_{ij}\beta _{j}(t+1)b^{v_{t+1}}_{j}(y_{t+1})}} -$$ - -But also inline i.e $z=x+y$ - -### Headings: third level - -Another paragraph. - - -# Examples of citations, figures, tables, references -\label{sec:others} - -You can insert references. Here is some text [@kour2014real; @kour2014fast] and see @hadash2018estimate. - -The documentation for \verb+natbib+ may be found at - -You can use custom blocks with LaTeX support from **rmarkdown** to create environment. - -::: {.center latex=true} - -::: - -Of note is the command \verb+\citet+, which produces citations -appropriate for use in inline text. - -You can insert LaTeX environment directly too. - -\begin{verbatim} - \citet{hasselmo} investigated\dots -\end{verbatim} - -produces - -\begin{quote} - Hasselmo, et al.\ (1995) investigated\dots -\end{quote} - -\begin{center} - \url{https://www.ctan.org/pkg/booktabs} -\end{center} - - -## Figures - -You can insert figure using LaTeX directly. - -See Figure \ref{fig:fig1}. Here is how you add footnotes. [^Sample of the first footnote.] - -\begin{figure} - \centering - \fbox{\rule[-.5cm]{4cm}{4cm} \rule[-.5cm]{4cm}{0cm}} - \caption{Sample figure caption.} - \label{fig:fig1} -\end{figure} - -But you can also do that using R. - -```{r fig2, fig.cap = "Another sample figure"} -plot(mtcars$mpg) -``` - -You can use **bookdown** to allow references for Tables and Figures. - - -## Tables - -Below we can see how to use tables. - -See awesome Table~\ref{tab:table} which is written directly in LaTeX in source Rmd file. - -\begin{table} - \caption{Sample table title} - \centering - \begin{tabular}{lll} - \toprule - \multicolumn{2}{c}{Part} \\ - \cmidrule(r){1-2} - Name & Description & Size ($\mu$m) \\ - \midrule - Dendrite & Input terminal & $\sim$100 \\ - Axon & Output terminal & $\sim$10 \\ - Soma & Cell body & up to $10^6$ \\ - \bottomrule - \end{tabular} - \label{tab:table} -\end{table} - -You can also use R code for that. - -```{r} -knitr::kable(head(mtcars), caption = "Head of mtcars table") -``` - - -## Lists - -- Item 1 -- Item 2 -- Item 3 diff --git a/papers/Collabra/paper/paper.pdf b/papers/Collabra/paper/paper.pdf deleted file mode 100644 index 0463f855d90bec7ff24af1fc4bc13132ec5658c5..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 313449 zcma&MbCf8(vo1Wg%{{hlTYGHVwr%aPZQHhO+qP%E{l4e?*1c<;Z>@X!k93kwI!RR} z_4Lz4A}1_L!$8XdMKZfMvoUN<`U1%k7RYHMvNMNU)0kb2~D8@KJsk-KA+YZh7K4x)Y5_HlEU6GVfVbkgj3U# zh1j|uWfWl&p;uTpzPyy?IZ`wYK?#-I#M;60F|wx0W}5RAJfIg$j>z57HWhXVfli!& zRS>^;k-FOYCV{^5?lF<_=%$fiZpBQk|MZUnB z1aH4;rB8scWy5QAdaK%?E{vXktL z$E;w)Xf2T{ntpCIMo#FLpYsx}PM^+~h@D!a?i0P4bdqx91Mf;~yPI-ssdxpijX)`2 zszhGQgHgy2V}ltl3=-a>H`y;fd@|uUNUp_!lsK|~X=MC>nNk4Wsjg+*u7q}E?!y>W8n+H7%7|51V!b-3edd}EUx zi0|J@eH>6d-hHDI`fTI*>sW^dAjNer8$xpbc+tvHi4ba=C7}@%CWCGTS0m7ds%GAR z!miuVgP?H3gEArY?F^!CEPa~Rgt`45uO{Wj=B~cH|iXud? za6SM8W+!kBECX0x6Es($JWquAV<^x*8jvc)`4t2MtY#5H8F%{KR{4cy!}U%hw>*k{ z*cFL0S0sZEVl9?n|6PJ=ev2$qAY(5!7;7l&r)~eZpB0{tm9?e3T*fY@7=3u=!7RUk 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-\usepackage{microtype} % microtypography -\usepackage{graphicx} - -\title{A template for the \emph{arxiv} style} - -\author{ - David S. Hippocampus - \thanks{Use footnote for providing further information about author -(webpage, alternative address)---\emph{not} for acknowledging funding -agencies. Optional.} - \\ - Department of Computer Science \\ - Cranberry-Lemon University \\ - Pittsburgh, PA 15213 \\ - \texttt{\href{mailto:hippo@cs.cranberry-lemon.edu}{\nolinkurl{hippo@cs.cranberry-lemon.edu}}} \\ - \And - Elias D. Striatum - \\ - Department of Electrical Engineering \\ - Mount-Sheikh University \\ - Santa Narimana, Levand \\ - \texttt{\href{mailto:stariate@ee.mount-sheikh.edu}{\nolinkurl{stariate@ee.mount-sheikh.edu}}} \\ - } - -% Pandoc syntax highlighting -\usepackage{color} -\usepackage{fancyvrb} -\newcommand{\VerbBar}{|} -\newcommand{\VERB}{\Verb[commandchars=\\\{\}]} -\DefineVerbatimEnvironment{Highlighting}{Verbatim}{commandchars=\\\{\}} -% Add ',fontsize=\small' for more characters per line -\usepackage{framed} -\definecolor{shadecolor}{RGB}{248,248,248} -\newenvironment{Shaded}{\begin{snugshade}}{\end{snugshade}} -\newcommand{\AlertTok}[1]{\textcolor[rgb]{0.94,0.16,0.16}{#1}} -\newcommand{\AnnotationTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textbf{\textit{#1}}}} -\newcommand{\AttributeTok}[1]{\textcolor[rgb]{0.77,0.63,0.00}{#1}} -\newcommand{\BaseNTok}[1]{\textcolor[rgb]{0.00,0.00,0.81}{#1}} -\newcommand{\BuiltInTok}[1]{#1} -\newcommand{\CharTok}[1]{\textcolor[rgb]{0.31,0.60,0.02}{#1}} -\newcommand{\CommentTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textit{#1}}} -\newcommand{\CommentVarTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textbf{\textit{#1}}}} -\newcommand{\ConstantTok}[1]{\textcolor[rgb]{0.00,0.00,0.00}{#1}} -\newcommand{\ControlFlowTok}[1]{\textcolor[rgb]{0.13,0.29,0.53}{\textbf{#1}}} -\newcommand{\DataTypeTok}[1]{\textcolor[rgb]{0.13,0.29,0.53}{#1}} -\newcommand{\DecValTok}[1]{\textcolor[rgb]{0.00,0.00,0.81}{#1}} -\newcommand{\DocumentationTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textbf{\textit{#1}}}} -\newcommand{\ErrorTok}[1]{\textcolor[rgb]{0.64,0.00,0.00}{\textbf{#1}}} -\newcommand{\ExtensionTok}[1]{#1} -\newcommand{\FloatTok}[1]{\textcolor[rgb]{0.00,0.00,0.81}{#1}} -\newcommand{\FunctionTok}[1]{\textcolor[rgb]{0.00,0.00,0.00}{#1}} -\newcommand{\ImportTok}[1]{#1} -\newcommand{\InformationTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textbf{\textit{#1}}}} -\newcommand{\KeywordTok}[1]{\textcolor[rgb]{0.13,0.29,0.53}{\textbf{#1}}} -\newcommand{\NormalTok}[1]{#1} -\newcommand{\OperatorTok}[1]{\textcolor[rgb]{0.81,0.36,0.00}{\textbf{#1}}} -\newcommand{\OtherTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{#1}} -\newcommand{\PreprocessorTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textit{#1}}} -\newcommand{\RegionMarkerTok}[1]{#1} -\newcommand{\SpecialCharTok}[1]{\textcolor[rgb]{0.00,0.00,0.00}{#1}} -\newcommand{\SpecialStringTok}[1]{\textcolor[rgb]{0.31,0.60,0.02}{#1}} -\newcommand{\StringTok}[1]{\textcolor[rgb]{0.31,0.60,0.02}{#1}} -\newcommand{\VariableTok}[1]{\textcolor[rgb]{0.00,0.00,0.00}{#1}} -\newcommand{\VerbatimStringTok}[1]{\textcolor[rgb]{0.31,0.60,0.02}{#1}} -\newcommand{\WarningTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textbf{\textit{#1}}}} - -% tightlist command for lists without linebreak -\providecommand{\tightlist}{% - \setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}} - -% From pandoc table feature -\usepackage{longtable,booktabs,array} -\usepackage{calc} % for calculating minipage widths -% Correct order of tables after \paragraph or \subparagraph -\usepackage{etoolbox} -\makeatletter -\patchcmd\longtable{\par}{\if@noskipsec\mbox{}\fi\par}{}{} -\makeatother -% Allow footnotes in longtable head/foot -\IfFileExists{footnotehyper.sty}{\usepackage{footnotehyper}}{\usepackage{footnote}} -\makesavenoteenv{longtable} - -% Pandoc citation processing -\newlength{\cslhangindent} -\setlength{\cslhangindent}{1.5em} -\newlength{\csllabelwidth} -\setlength{\csllabelwidth}{3em} -\newlength{\cslentryspacingunit} % times entry-spacing -\setlength{\cslentryspacingunit}{\parskip} -% for Pandoc 2.8 to 2.10.1 -\newenvironment{cslreferences}% - {}% - {\par} -% For Pandoc 2.11+ -\newenvironment{CSLReferences}[2] % #1 hanging-ident, #2 entry spacing - {% don't indent paragraphs - \setlength{\parindent}{0pt} - % turn on hanging indent if param 1 is 1 - \ifodd #1 - \let\oldpar\par - \def\par{\hangindent=\cslhangindent\oldpar} - \fi - % set entry spacing - \setlength{\parskip}{#2\cslentryspacingunit} - }% - {} -\usepackage{calc} -\newcommand{\CSLBlock}[1]{#1\hfill\break} -\newcommand{\CSLLeftMargin}[1]{\parbox[t]{\csllabelwidth}{#1}} -\newcommand{\CSLRightInline}[1]{\parbox[t]{\linewidth - \csllabelwidth}{#1}\break} -\newcommand{\CSLIndent}[1]{\hspace{\cslhangindent}#1} - -\begin{document} -\maketitle - - -\begin{abstract} -Enter the text of your abstract here. -\end{abstract} - -\keywords{ - blah - \and - blee - \and - bloo - \and - these are optional and can be removed - } - -\hypertarget{introduction}{% -\section{Introduction}\label{introduction}} - -Here goes an introduction text - -\hypertarget{headings-first-level}{% -\section{Headings: first level}\label{headings-first-level}} - -\label{sec:headings} - -You can use directly LaTeX command or Markdown text. - -LaTeX command can be used to reference other section. See Section -\ref{sec:headings}. However, you can also use \textbf{bookdown} -extensions mechanism for this. - -\hypertarget{headings-second-level}{% -\subsection{Headings: second level}\label{headings-second-level}} - -You can use equation in blocks - -\[ -\xi _{ij}(t)=P(x_{t}=i,x_{t+1}=j|y,v,w;\theta)= {\frac {\alpha _{i}(t)a^{w_t}_{ij}\beta _{j}(t+1)b^{v_{t+1}}_{j}(y_{t+1})}{\sum _{i=1}^{N} \sum _{j=1}^{N} \alpha _{i}(t)a^{w_t}_{ij}\beta _{j}(t+1)b^{v_{t+1}}_{j}(y_{t+1})}} -\] - -But also inline i.e \(z=x+y\) - -\hypertarget{headings-third-level}{% -\subsubsection{Headings: third level}\label{headings-third-level}} - -Another paragraph. - -\hypertarget{examples-of-citations-figures-tables-references}{% -\section{Examples of citations, figures, tables, -references}\label{examples-of-citations-figures-tables-references}} - -\label{sec:others} - -You can insert references. Here is some text (Kour and Saabne 2014b, -2014a) and see Hadash et al. (2018). - -The documentation for \verb+natbib+ may be found at - -You can use custom blocks with LaTeX support from \textbf{rmarkdown} to -create environment. - -\begin{center} -\url{http://mirrors.ctan.org/macros/latex/contrib/natbib/natnotes.pdf\%7D} - -\end{center} - -Of note is the command \verb+\citet+, which produces citations -appropriate for use in inline text. - -You can insert LaTeX environment directly too. - -\begin{verbatim} - \citet{hasselmo} investigated\dots -\end{verbatim} - -produces - -\begin{quote} - Hasselmo, et al.\ (1995) investigated\dots -\end{quote} - -\begin{center} - \url{https://www.ctan.org/pkg/booktabs} -\end{center} - -\hypertarget{figures}{% -\subsection{Figures}\label{figures}} - -You can insert figure using LaTeX directly. - -See Figure \ref{fig:fig1}. Here is how you add footnotes. {[}\^{}Sample -of the first footnote.{]} - -\begin{figure} - \centering - \fbox{\rule[-.5cm]{4cm}{4cm} \rule[-.5cm]{4cm}{0cm}} - \caption{Sample figure caption.} - \label{fig:fig1} -\end{figure} - -But you can also do that using R. - -\begin{Shaded} -\begin{Highlighting}[] -\FunctionTok{plot}\NormalTok{(mtcars}\SpecialCharTok{$}\NormalTok{mpg)} -\end{Highlighting} -\end{Shaded} - -\begin{figure} -\centering -\includegraphics{paper_files/figure-latex/fig2-1.pdf} -\caption{Another sample figure} -\end{figure} - -You can use \textbf{bookdown} to allow references for Tables and -Figures. - -\hypertarget{tables}{% -\subsection{Tables}\label{tables}} - -Below we can see how to use tables. - -See awesome Table\textasciitilde{}\ref{tab:table} which is written -directly in LaTeX in source Rmd file. - -\begin{table} - \caption{Sample table title} - \centering - \begin{tabular}{lll} - \toprule - \multicolumn{2}{c}{Part} \\ - \cmidrule(r){1-2} - Name & Description & Size ($\mu$m) \\ - \midrule - Dendrite & Input terminal & $\sim$100 \\ - Axon & Output terminal & $\sim$10 \\ - Soma & Cell body & up to $10^6$ \\ - \bottomrule - \end{tabular} - \label{tab:table} -\end{table} - -You can also use R code for that. - -\begin{Shaded} -\begin{Highlighting}[] -\NormalTok{knitr}\SpecialCharTok{::}\FunctionTok{kable}\NormalTok{(}\FunctionTok{head}\NormalTok{(mtcars), }\AttributeTok{caption =} \StringTok{"Head of mtcars table"}\NormalTok{)} -\end{Highlighting} -\end{Shaded} - -\begin{longtable}[]{@{} - >{\raggedright\arraybackslash}p{(\columnwidth - 22\tabcolsep) * \real{0.2609}} - >{\raggedleft\arraybackslash}p{(\columnwidth - 22\tabcolsep) * \real{0.0725}} - >{\raggedleft\arraybackslash}p{(\columnwidth - 22\tabcolsep) * \real{0.0580}} - >{\raggedleft\arraybackslash}p{(\columnwidth - 22\tabcolsep) * \real{0.0725}} - >{\raggedleft\arraybackslash}p{(\columnwidth - 22\tabcolsep) * \real{0.0580}} - >{\raggedleft\arraybackslash}p{(\columnwidth - 22\tabcolsep) * \real{0.0725}} - >{\raggedleft\arraybackslash}p{(\columnwidth - 22\tabcolsep) * \real{0.0870}} - >{\raggedleft\arraybackslash}p{(\columnwidth - 22\tabcolsep) * \real{0.0870}} - >{\raggedleft\arraybackslash}p{(\columnwidth - 22\tabcolsep) * \real{0.0435}} - >{\raggedleft\arraybackslash}p{(\columnwidth - 22\tabcolsep) * \real{0.0435}} - >{\raggedleft\arraybackslash}p{(\columnwidth - 22\tabcolsep) * \real{0.0725}} - >{\raggedleft\arraybackslash}p{(\columnwidth - 22\tabcolsep) * \real{0.0725}}@{}} -\caption{Head of mtcars table}\tabularnewline -\toprule() -\begin{minipage}[b]{\linewidth}\raggedright -\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft -mpg -\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft -cyl -\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft -disp -\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft -hp -\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft -drat -\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft -wt -\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft -qsec -\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft -vs -\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft -am -\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft -gear -\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft -carb -\end{minipage} \\ -\midrule() -\endfirsthead -\toprule() -\begin{minipage}[b]{\linewidth}\raggedright -\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft -mpg -\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft -cyl -\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft -disp -\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft -hp -\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft -drat -\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft -wt -\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft -qsec -\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft -vs -\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft -am -\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft -gear -\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft -carb -\end{minipage} \\ -\midrule() -\endhead -Mazda RX4 & 21.0 & 6 & 160 & 110 & 3.90 & 2.620 & 16.46 & 0 & 1 & 4 & -4 \\ -Mazda RX4 Wag & 21.0 & 6 & 160 & 110 & 3.90 & 2.875 & 17.02 & 0 & 1 & 4 -& 4 \\ -Datsun 710 & 22.8 & 4 & 108 & 93 & 3.85 & 2.320 & 18.61 & 1 & 1 & 4 & -1 \\ -Hornet 4 Drive & 21.4 & 6 & 258 & 110 & 3.08 & 3.215 & 19.44 & 1 & 0 & 3 -& 1 \\ -Hornet Sportabout & 18.7 & 8 & 360 & 175 & 3.15 & 3.440 & 17.02 & 0 & 0 -& 3 & 2 \\ -Valiant & 18.1 & 6 & 225 & 105 & 2.76 & 3.460 & 20.22 & 1 & 0 & 3 & 1 \\ -\bottomrule() -\end{longtable} - -\hypertarget{lists}{% -\subsection{Lists}\label{lists}} - -\begin{itemize} -\tightlist -\item - Item 1 -\item - Item 2 -\item - Item 3 -\end{itemize} - -\hypertarget{refs}{} -\begin{CSLReferences}{1}{0} -\leavevmode\vadjust pre{\hypertarget{ref-hadash2018estimate}{}}% -Hadash, Guy, Einat Kermany, Boaz Carmeli, Ofer Lavi, George Kour, and -Alon Jacovi. 2018. {``Estimate and Replace: A Novel Approach to -Integrating Deep Neural Networks with Existing Applications.''} -\emph{arXiv Preprint arXiv:1804.09028}. - -\leavevmode\vadjust pre{\hypertarget{ref-kour2014fast}{}}% -Kour, George, and Raid Saabne. 2014a. {``Fast Classification of -Handwritten on-Line Arabic Characters.''} In \emph{Soft Computing and -Pattern Recognition (SoCPaR), 2014 6th International Conference of}, -312--18. IEEE. - -\leavevmode\vadjust pre{\hypertarget{ref-kour2014real}{}}% ----------. 2014b. {``Real-Time Segmentation of on-Line Handwritten -Arabic Script.''} In \emph{Frontiers in Handwriting Recognition (ICFHR), -2014 14th International Conference on}, 417--22. IEEE. - -\end{CSLReferences} - -\bibliographystyle{unsrt} -\bibliography{references.bib} - - -\end{document} diff --git a/papers/Collabra/paper/paper_files/figure-latex/fig2-1.pdf b/papers/Collabra/paper/paper_files/figure-latex/fig2-1.pdf deleted file mode 100644 index b793fa72fcc4e75c51dd050fd513a1356e196025..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 6205 zcmZ{ocOYC__xB~PxCnya>O<5phEYdN^b%2{jyeVtW(G5QFF_0vq6E=fLPU>FBua$Q zqlbhby67$O8}7}0?(^LDJ^!7x*V=3Cwf8yabG|%!Dr!JcVR3Svkhzfgkp7Tis5`kR zKm>rcyH74BM-EbUhudNiXq1XA77pN7kpYW<#YDtKz@lOz(qiHQU0o-ECc+5HJit*8}V7fhC0LxufkpU~u>IQE_3gFqmMw$b~*P36Lu&ki${-=T(6J zt_A=y@^OU&K+3jQTNkt=0HkN@2*&`#2o45-{{%?=E8yJk+}j;cXGam3?8 zCGZIl_&okWK-(i__C6;KO%NLWx~X|qVP*!!QL8XC^SY{V^tG?mvXBKkWUuna?)?7x z{+IoaMXje_R@c+LYUS5YT1wAaPZs-gld*Ij%8?hqL5_M zi+C^WowdwYJg+sk98ieGdIhZG@e z_G7MTt4d++t_J%G{FH<#UEC)_3%m62@m?KSADYH(2jGH+^66?4RSV;NZl&Z%gI9^^ zs?WC#)ntmblgkzpG2_mf9(Dqp=h+{8B)0Hl7L(*Qikn998QO4oS257kNq2^rKku$o 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zJhb*SVoh}XN*&e`>y0gLfARm*4c-G@q*%g?*t82Roist=#HV-(4 z<&81W1@8&6w-0mavhFTsJyS^XSXo~FIt**p_T7B;P##kXYC>H{;{drCJQCf7%Sg7*P8)bErA`B<+ADQ2a-QW2^`aB2 z->ldaRD2rv?dXr)?;Axix>|3YoZ-xx~%mtd=kB50!s6hW~)$JYPcnIKTN zQ5eK8135?q;otx#sI=!YtOY<^0)#}MJTL&uf5^cXApMJS|I~voFdJm(VTZkthtG`! ze!pvrB)~5Ly)Tmf>7xO6@q}X$Fk5oaucUzUa{nnGd%MFO$VC96qU0ifUjRu72{8$P z1K@8Pm>`m$UjWqKHc?5!PsV@Sz*3NZ+oYukp#DF85NU$S{NFY)g2?{AHiC&DhyS;q z2pIA&n}n3;zj8=OpSSK;EY{r?;R1IjX#4<>A;K3 Date: Mon, 10 Apr 2023 09:06:45 +0100 Subject: [PATCH 04/34] minor cover letter + ms --- papers/Collabra/cover_letter.Rmd | 15 +++++++++------ papers/Collabra/paper.Rmd | 13 +++++++++---- 2 files changed, 18 insertions(+), 10 deletions(-) diff --git a/papers/Collabra/cover_letter.Rmd b/papers/Collabra/cover_letter.Rmd index 700385be2..b3d323350 100644 --- a/papers/Collabra/cover_letter.Rmd +++ b/papers/Collabra/cover_letter.Rmd @@ -2,21 +2,24 @@ output: pdf_document --- -Dear Editors, +Dear Editor, -We are pleased to submit this paper to *Mathematics*, for the special issue "Advances in Statistical Computing". +We are pleased to submit this paper to [TODO]. -The paper, titled "Check your outliers! An accessible introduction to identifying statistical outliers in R with *easystats*", provides an overview of current recommendations and best practices regarding the diagnosis and treament of outliers. It demonstrates how these recommendations can be easily and conveniently implemented in the R software using the *{performance}* package of the *easystats* ecosystem. The manuscript covers univariate, multivariate, and model-based statistical outlier detection methods, their recommended threshold, standard output, and plotting method, among other things. +The paper, titled "Check your outliers! An accessible introduction to identifying statistical outliers in R with *easystats*", provides an overview of current recommendations and best practices regarding the diagnosis and treatment of outliers, a common issue faced by researchers - and a potential source of scientific malpractice. -In this sense, the paper fits very well with the special issue "Advances in Statistical Computing", as it essentially communicates to the wider public current advances in the statistical computing of outlier detection algorithms and their implementation in currently available open source and free software. This makes the manuscript relevant to data science, behavioural science, and statistical computing more generally. +It explains the key approaches and highlights recommendations, and shows how users can adopt them in their R analysis with just one function. The manuscript covers univariate, multivariate, and model-based statistical outlier detection methods, their recommended threshold, standard output, and plotting method, among other things. + +Beyond acting like a concise review of outlier treatment procedures and practical tutorial, we also describe a new method (a consensus-based approach) and discuss its benefits ad limitations. In this sense, the paper fits very well with the scope of the journal, as it essentially communicates to the wider public current advances in the statistical computing of outlier detection algorithms and their implementation in currently available open source and free software. This makes the manuscript relevant to data science, behavioural science, and statistical computing more generally. + Our current submission is original and has been neither published elsewhere nor is currently under consideration for publication elsewhere. All authors have contributed substantially to the software and manuscript. All authors gave final approval to the manuscript and accept to be accountable. We have no conflicts of interest to disclose. -We would also like to use the open peer review option. + Thank you for considering our submission. -Best Regards, +On the behalf of all authors, Rémi Thériault diff --git a/papers/Collabra/paper.Rmd b/papers/Collabra/paper.Rmd index 4208cb67a..87ca0b997 100644 --- a/papers/Collabra/paper.Rmd +++ b/papers/Collabra/paper.Rmd @@ -109,7 +109,7 @@ library(datawizard) # Introduction -Real-life data often contain observations that can be considered *abnormal* when compared to the main population. The cause of it---be it because they belong to a different distribution (originating from a different generative process) or simply being extreme cases, statistically rare but not impossible---can be hard to assess, and the boundaries of "abnormal" are hard to define. +Real-life data often contain observations that can be considered *abnormal* when compared to the main population. The cause of it---be it because they belong to a different distribution (originating from a different generative process) or simply being extreme cases, statistically rare but not impossible---can be hard to assess, and the boundaries of "abnormal" difficult to define. Nonetheless, the improper handling of these outliers can substantially affect statistical model estimations, biasing effect estimations and weakening the models' predictive performance. It is thus essential to address this problem in a thoughtful manner. Yet, despite the existence of established recommendations and guidelines, many researchers still do not treat outliers in a consistent manner, or do so using inappropriate strategies [@simmons2011false; @leys2013outliers]. @@ -236,7 +236,8 @@ knitr::kable( caption = "Summary of Statistical Outlier Detection Methods Recommendations.", longtable = TRUE) ``` -### Cook's Distance vs. MCD + + @leys2018outliers report a preference for the MCD method over Cook's distance. This is because Cook's distance removes one observation at a time and checks its corresponding influence on the model each time [@cook1977detection], and flags any observation that has a large influence. In the view of these authors, when there are several outliers, the process of removing a single outlier at a time is problematic as the model remains "contaminated" or influenced by other possible outliers in the model, rendering this method suboptimal in the presence of multiple outliers. @@ -268,9 +269,9 @@ plot(outliers) Finally, unusual observations happen naturally: extreme observations are expected even when taken from a normal distribution. While statistical models can integrate this "expectation", multivariate outlier methods might be too conservative, flagging too many observations despite belonging to the right generative process. For these reasons, we believe that model-based methods are still preferable to the MCD when using supported regression models. Additionally, if the presence of multiple outliers is a significant concern, regression methods that are more robust to outliers should be considered---like _t_ regression or quantile regression---as they render their precise identification less critical [@mcelreath2020statistical]. -## Multiple Methods +## Composite Outlier Score -An alternative approach that is possible is to combine several methods, based on the assumption that different methods provide different angles of looking at the problem. By applying a variety of methods, one can hope to "triangulate" the true outliers (those consistently flagged by multiple methods) and thus attempt to minimize false positives. +An alternative approach that to adopt a consensus-based approach by combining several methods, based on the assumption that different methods provide different angles of looking at the problem. By applying a variety of methods, one can hope to "triangulate" the true outliers (those consistently flagged by multiple methods) and thus attempt to minimize false positives. In practice, this approach computes a composite outlier score, formed of the average of the binary (0 or 1) classification results of each method. It represents the probability that each observation is classified as an outlier by at least one method. The default decision rule classifies rows with composite outlier scores superior or equal to 0.5 as outlier observations (i.e., that were classified as outliers by at least half of the methods). In *{performance}*'s `check_outliers()`, one can use this approach by including all desired methods in the corresponding argument. @@ -322,6 +323,10 @@ winsorized_data[1501:1502, ] Once again, it is a critical part of a sound outlier treatment that regardless of which SOD method used, it should be reported in a reproducible manner. Ideally, the handling of outliers should be specified *a priori* with as much detail as possible, and preregistered, to limit researchers' degrees of freedom and therefore risks of false positives [@leys2019outliers]. This is especially true given that interesting outliers and random outliers are often times hard to distinguish in practice. Thus, researchers should always prioritize transparency and report all of the following information: (a) how many outliers were identified; (b) according to which method and criteria, (c) using which function of which R package (if applicable), and (d) how they were handled (excluded or winsorized, if the latter, using what threshold). If at all possible, (e) the corresponding code script along with the data should be shared on a public repository like the Open Science Framework (OSF), so that the exclusion criteria can be reproduced precisely. +## What happens ater? + +See comment in the thread. + # Conclusion In this paper, we have showed how to investigate outliers using the `check_outliers()` function of the *{performance}* package while following current good practices. However, best practice for outlier treatment does not stop at using appropriate statistical algorithms, but entails respecting existing recommendations, such as preregistration, reproducibility, consistency, transparency, and justification. Ideally, one would additionally also report the package, function, and threshold used (linking to the full code when possible). We hope that this paper and the accompanying `check_outlier()` function of *easystats* will help researchers engage in good research practices while providing a smooth outlier detection experience. From 45362eff73bb3ae4abec06375cb6c37d79e70b70 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?R=C3=A9mi=20Th=C3=A9riault?= <13123390+rempsyc@users.noreply.github.com> Date: Mon, 17 Apr 2023 12:48:45 -0400 Subject: [PATCH 05/34] integrate dom comments [skip ci] --- papers/Collabra/mybibfile.bib | 15 +++++++-------- papers/Collabra/paper.Rmd | 13 ++++--------- 2 files changed, 11 insertions(+), 17 deletions(-) diff --git a/papers/Collabra/mybibfile.bib b/papers/Collabra/mybibfile.bib index 463fd9e2b..32e8e0783 100644 --- a/papers/Collabra/mybibfile.bib +++ b/papers/Collabra/mybibfile.bib @@ -41,14 +41,13 @@ @article{simmons2011false URL = {https://doi.org/10.1177/0956797611417632}, } -@Article{easystatspackage, - title = {easystats: Framework for Easy Statistical Modeling, Visualization, and Reporting}, - author = {Daniel Lüdecke and Mattan S. Ben-Shachar and Indrajeet Patil and Brenton M. Wiernik and Etienne Bacher and Rémi Thériault and Dominique Makowski}, - journal = {CRAN}, - year = {2022}, - note = {R package}, - url = {https://easystats.github.io/easystats/}, - } +@software{easystatspackage, + title = {{easystats}: Streamline Model Interpretation, Visualization, and Reporting}, + author = {Daniel Lüdecke and Dominique Makowski and Mattan S. Ben-Shachar and Indrajeet Patil and Brenton M. Wiernik and Etienne Bacher and Rémi Thériault}, + date = {2023-02-04T22:06:06Z}, + origdate = {2019-01-28T10:39:29Z}, + url = {https://easystats.github.io/easystats/} +} @Article{ludecke2021performance, author = {Daniel Lüdecke and Mattan S. Ben-Shachar and Indrajeet Patil and Philip Waggoner and Dominique Makowski}, diff --git a/papers/Collabra/paper.Rmd b/papers/Collabra/paper.Rmd index 87ca0b997..b227519f3 100644 --- a/papers/Collabra/paper.Rmd +++ b/papers/Collabra/paper.Rmd @@ -236,8 +236,7 @@ knitr::kable( caption = "Summary of Statistical Outlier Detection Methods Recommendations.", longtable = TRUE) ``` - - +## Cook's Distance vs. MCD @leys2018outliers report a preference for the MCD method over Cook's distance. This is because Cook's distance removes one observation at a time and checks its corresponding influence on the model each time [@cook1977detection], and flags any observation that has a large influence. In the view of these authors, when there are several outliers, the process of removing a single outlier at a time is problematic as the model remains "contaminated" or influenced by other possible outliers in the model, rendering this method suboptimal in the presence of multiple outliers. @@ -271,7 +270,7 @@ Finally, unusual observations happen naturally: extreme observations are expecte ## Composite Outlier Score -An alternative approach that to adopt a consensus-based approach by combining several methods, based on the assumption that different methods provide different angles of looking at the problem. By applying a variety of methods, one can hope to "triangulate" the true outliers (those consistently flagged by multiple methods) and thus attempt to minimize false positives. +The *{performance}* package also offers an alternative, consensus-based approach that combines several methods, based on the assumption that different methods provide different angles of looking at a given problem. By applying a variety of methods, one can hope to "triangulate" the true outliers (those consistently flagged by multiple methods) and thus attempt to minimize false positives. In practice, this approach computes a composite outlier score, formed of the average of the binary (0 or 1) classification results of each method. It represents the probability that each observation is classified as an outlier by at least one method. The default decision rule classifies rows with composite outlier scores superior or equal to 0.5 as outlier observations (i.e., that were classified as outliers by at least half of the methods). In *{performance}*'s `check_outliers()`, one can use this approach by including all desired methods in the corresponding argument. @@ -298,7 +297,7 @@ The above section demonstrated how to identify outliers using the `check_outlier @leys2019outliers distinguish between error outliers, interesting outliers, and random outliers. _Error outliers_ are likely due to human error and should be corrected before data analysis or outright removed since they are invalid observations. _Interesting outliers_ are not due to technical error and may be of theoretical interest; it might thus be relevant to investigate them further even though they should be removed from the current analysis of interest. _Random outliers_ are assumed to be due to chance alone and to belong to the correct distribution and, therefore, should be retained. -It is recommended to _keep_ observations which are expected to be part of the distribution of interest, even if they are outliers [@leys2019outliers]. However, if it is suspected that the outliers belong to an alternative distribution, then those observations could have a large impact on the results and call into question their robustness, especially if significance is conditional on their inclusion. +It is recommended to _keep_ observations which are expected to be part of the distribution of interest, even if they are outliers [@leys2019outliers]. However, if it is suspected that the outliers belong to an alternative distribution, then those observations could have a large impact on the results and call into question their robustness, especially if significance is conditional on their inclusion, so should be removed. On the other hand, there are also outliers that cannot be detected by statistical tools, but should be found and removed. For example, if we are studying the effects of X on Y among teenagers and we have one observation from a 20-year-old, this observation might not be a _statistical outlier_, but it is an outlier in the _context_ of our research, and should be discarded to allow for valid inferences. @@ -321,11 +320,7 @@ winsorized_data[1501:1502, ] ## The Importance of Transparency -Once again, it is a critical part of a sound outlier treatment that regardless of which SOD method used, it should be reported in a reproducible manner. Ideally, the handling of outliers should be specified *a priori* with as much detail as possible, and preregistered, to limit researchers' degrees of freedom and therefore risks of false positives [@leys2019outliers]. This is especially true given that interesting outliers and random outliers are often times hard to distinguish in practice. Thus, researchers should always prioritize transparency and report all of the following information: (a) how many outliers were identified; (b) according to which method and criteria, (c) using which function of which R package (if applicable), and (d) how they were handled (excluded or winsorized, if the latter, using what threshold). If at all possible, (e) the corresponding code script along with the data should be shared on a public repository like the Open Science Framework (OSF), so that the exclusion criteria can be reproduced precisely. - -## What happens ater? - -See comment in the thread. +Once again, it is a critical part of a sound outlier treatment that regardless of which SOD method used, it should be reported in a reproducible manner. Ideally, the handling of outliers should be specified *a priori* with as much detail as possible, and preregistered, to limit researchers' degrees of freedom and therefore risks of false positives [@leys2019outliers]. This is especially true given that interesting outliers and random outliers are often times hard to distinguish in practice. Thus, researchers should always prioritize transparency and report all of the following information: (a) how many outliers were identified (including percentage); (b) according to which method and criteria, (c) using which function of which R package (if applicable), and (d) how they were handled (excluded or winsorized, if the latter, using what threshold). If at all possible, (e) the corresponding code script along with the data should be shared on a public repository like the Open Science Framework (OSF), so that the exclusion criteria can be reproduced precisely. # Conclusion From 068804a207ddd6e32fd6219eb8974674c7155ed4 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?R=C3=A9mi=20Th=C3=A9riault?= <13123390+rempsyc@users.noreply.github.com> Date: Mon, 17 Apr 2023 17:53:10 -0400 Subject: [PATCH 06/34] update cover letter, response to reviewers [skip ci] --- papers/Collabra/apa.csl | 1917 +++++++++++++++++ papers/Collabra/cover_letter.Rmd | 15 +- papers/Collabra/cover_letter.pdf | Bin 0 -> 56483 bytes papers/Collabra/mybibfile.bib | 2 +- papers/Collabra/paper.Rmd | 19 +- papers/Collabra/paper.pdf | Bin 388564 -> 423868 bytes papers/Collabra/paper.tex | 220 +- .../Collabra/paper_files/Editor comments.pdf | Bin 0 -> 190532 bytes papers/Collabra/paper_files/Editor email.pdf | Bin 0 -> 480178 bytes .../paper_files/Reviewer 1 comments.pdf | Bin 0 -> 168997 bytes .../paper_files/Reviewer 2 comments.pdf | Bin 0 -> 182989 bytes .../paper_files/Reviewer 3 comments.pdf | Bin 0 -> 167380 bytes .../paper_files/Reviewer comments.pdf | Bin 0 -> 423076 bytes .../paper_files/Reviewer comments_short.pdf | Bin 0 -> 374787 bytes papers/Collabra/paper_files/Tite page.pdf | Bin 0 -> 51806 bytes .../paper_files/figure-latex/model-1.pdf | Bin 7820 -> 7821 bytes .../paper_files/figure-latex/model2-1.pdf | Bin 8531 -> 8530 bytes .../figure-latex/multivariate_implicit-1.pdf | Bin 5104 -> 5104 bytes .../paper_files/figure-latex/scatter-1.pdf | Bin 7724 -> 7724 bytes .../figure-latex/univariate_implicit-1.pdf | Bin 5117 -> 5117 bytes papers/Collabra/reviewer_response.Rmd | 83 + papers/Collabra/reviewer_response.pdf | Bin 0 -> 92048 bytes papers/Mathematics/paper.pdf | Bin 250727 -> 250713 bytes papers/Mathematics/paper.tex | 2 +- .../paper_files/figure-latex/model-1.pdf | Bin 7824 -> 7822 bytes .../paper_files/figure-latex/model2-1.pdf | Bin 8536 -> 8535 bytes .../figure-latex/multivariate-1.pdf | Bin 5096 -> 5096 bytes .../paper_files/figure-latex/scatter-1.pdf | Bin 7724 -> 7724 bytes .../paper_files/figure-latex/univariate-1.pdf | Bin 5097 -> 5097 bytes 29 files changed, 2149 insertions(+), 109 deletions(-) create mode 100644 papers/Collabra/apa.csl create mode 100644 papers/Collabra/cover_letter.pdf create mode 100644 papers/Collabra/paper_files/Editor comments.pdf create mode 100644 papers/Collabra/paper_files/Editor email.pdf create mode 100644 papers/Collabra/paper_files/Reviewer 1 comments.pdf create mode 100644 papers/Collabra/paper_files/Reviewer 2 comments.pdf create mode 100644 papers/Collabra/paper_files/Reviewer 3 comments.pdf create mode 100644 papers/Collabra/paper_files/Reviewer comments.pdf create mode 100644 papers/Collabra/paper_files/Reviewer comments_short.pdf create mode 100644 papers/Collabra/paper_files/Tite page.pdf create mode 100644 papers/Collabra/reviewer_response.Rmd create mode 100644 papers/Collabra/reviewer_response.pdf diff --git a/papers/Collabra/apa.csl b/papers/Collabra/apa.csl new file mode 100644 index 000000000..946c7fcd2 --- /dev/null +++ b/papers/Collabra/apa.csl @@ -0,0 +1,1917 @@ + + \ No newline at end of file diff --git a/papers/Collabra/cover_letter.Rmd b/papers/Collabra/cover_letter.Rmd index b3d323350..4251c050a 100644 --- a/papers/Collabra/cover_letter.Rmd +++ b/papers/Collabra/cover_letter.Rmd @@ -2,20 +2,19 @@ output: pdf_document --- -Dear Editor, +Dear Dr. Vazire, -We are pleased to submit this paper to [TODO]. +We are pleased to submit this paper to *Collabra: Psychology*. -The paper, titled "Check your outliers! An accessible introduction to identifying statistical outliers in R with *easystats*", provides an overview of current recommendations and best practices regarding the diagnosis and treatment of outliers, a common issue faced by researchers - and a potential source of scientific malpractice. +The paper, titled "Check your outliers! An introduction to identifying statistical outliers in R with *easystats*", provides an overview of current recommendations and best practices regarding the diagnosis and treatment of outliers, a common issue faced by researchers---and a potential source of scientific malpractice. -It explains the key approaches and highlights recommendations, and shows how users can adopt them in their R analysis with just one function. The manuscript covers univariate, multivariate, and model-based statistical outlier detection methods, their recommended threshold, standard output, and plotting method, among other things. +It explains the key approaches, highlights recommendations, and shows how users can adopt them in their R analysis with a single function. The manuscript covers univariate, multivariate, and model-based statistical outlier detection methods, their recommended threshold, standard output, and plotting method, among other things. -Beyond acting like a concise review of outlier treatment procedures and practical tutorial, we also describe a new method (a consensus-based approach) and discuss its benefits ad limitations. In this sense, the paper fits very well with the scope of the journal, as it essentially communicates to the wider public current advances in the statistical computing of outlier detection algorithms and their implementation in currently available open source and free software. This makes the manuscript relevant to data science, behavioural science, and statistical computing more generally. - +Beyond acting like a concise review of outlier treatment procedures and practical tutorial, we also introduce a new outlier-detection method that relies on a consensus-based approach. In this sense, the paper fits well with the "Methodology and Research Practice in Psychology" section of the journal, as it essentially communicates to psychologists how to easily follow some of the best practices in the detection of statistical outlier using currently available open source and free software. This makes the manuscript relevant to data science, behavioural science, and good research and statistical practices more generally. -Our current submission is original and has been neither published elsewhere nor is currently under consideration for publication elsewhere. All authors have contributed substantially to the software and manuscript. All authors gave final approval to the manuscript and accept to be accountable. We have no conflicts of interest to disclose. +As Associated Editor, we would like to suggest Jeffrey Girard, as he is familiar with the *easystats* and R ecosystems, as well as good statistical practices. Additionally, we would like to request a streamlined review, as the manuscript has been rejected within the previous 365 days from the journal *Mathematics*. Accordingly, we provide in this submission a detailed letter that includes prior reviews, the decision letter, as well as how we addressed the reviewers' comments. We have in this regard integrated most of the changes suggested by the reviewers. Note that the previous editors and reviewers have not given their permission for their comments to be openly available at *Collabra: Psychology*. However, although an open review was requested, the reviewers did not sign their reviews. - +Our current submission is original and has been neither published elsewhere nor is currently under consideration for publication elsewhere. All authors have contributed substantially to the software and manuscript. All authors gave final approval to the manuscript and accept to be accountable. We have no conflicts of interest to disclose. We have also read the Transparency and Openness policy of the Editorial Policies of *Collabra: Psychology*. 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algorithms ((a) median absolute deviation (MAD)-based robust _z_ scores, [@leys2013outliers]; (b) Mahalanobis minimum covariance determinant (MCD), [@leys2019outliers]; and (c) Cook's distance, [@cook1977detection]), we excluded two participants that were classified as outliers by at least half of the methods used. +> Based on a composite outlier score [see the 'check_outliers()' function in the 'performance' R package, @ludecke2021performance] obtained via the joint application of multiple outliers detection algorithms [(a) median absolute deviation (MAD)-based robust _z_ scores, @leys2013outliers; (b) Mahalanobis minimum covariance determinant (MCD), @leys2019outliers; and (c) Cook's distance, @cook1977detection], we excluded two participants that were classified as outliers by at least half of the methods used. # Handling Outliers @@ -326,4 +327,20 @@ Once again, it is a critical part of a sound outlier treatment that regardless o In this paper, we have showed how to investigate outliers using the `check_outliers()` function of the *{performance}* package while following current good practices. However, best practice for outlier treatment does not stop at using appropriate statistical algorithms, but entails respecting existing recommendations, such as preregistration, reproducibility, consistency, transparency, and justification. Ideally, one would additionally also report the package, function, and threshold used (linking to the full code when possible). We hope that this paper and the accompanying `check_outlier()` function of *easystats* will help researchers engage in good research practices while providing a smooth outlier detection experience. +### Contributions + +Author 1 drafted the paper; all authors contributed to both the writing of the paper and the conception of the software. + +### Acknowledgements + +*{performance}* is part of the collaborative [*easystats*](https://github.com/easystats/easystats) ecosystem [@easystatspackage]. Thus, we thank all [members of easystats](https://github.com/orgs/easystats/people), contributors, and users alike. + +### Funding information + +This research received no external funding. + +### Competing Interests + +The authors declare no conflict of interest + # References \ No newline at end of file diff --git a/papers/Collabra/paper.pdf b/papers/Collabra/paper.pdf index ae0831cfc31055798c10ba0b990945a34e4f464d..0a439a6cfa326b7b469af3e47b81fd0fafb8f231 100644 GIT binary patch delta 228312 zcmc$`1yogC*EURdO9)Z|(s2$P8focnM4Cf)_ZCD_K~fMw2~k1;5s)rvK|(;fLplU$ z{&SAEw|K|D9{%5k z@{d0HV<-s!cY=573NH|&LI{Eo|G%>IpVDi?Z-^Ky;;slMg8mxE54Q#WeX0A+iuiuH z>?H?KfOqjrvj_|MwOAmu{U6p9nEfF}`cDfB-(^Sr7h~u9eP!YMM?bv<7ZWjlMDa@< zoQU=Br@|EBmm!4yrS~6NgID}AC4|7g2FD4n{dteSDC6g8E%-HmsY8eXAm;w(W$N(D z{h^6y^$r<3z> z|7KMX2=GsflMcKyTX^x)O%Yy-n4iD+3Sxc`BK^|tZw`)ViI5cW*!!tzL>I8eF#G$} z5HWCsA0p2EntQ}#BW~;WrvpL$bs_j8RQPQm0sQ}yyZ$cJ zFQWutVHE#AI<3^73PG&$h$%qG=mW1nC<$R5h(!mn${-FA_JR2I%abq3_*b6+{tWP7 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zXmlV3Xy`|}sQ^~W&IU;B#!t5c?Px^rzpvQDbG4N=?giLu_M>yxPwO915U9;;z} z>l5LOXTkU)%2N-+E8L2~$v$vZ%oQEVwm2BjqR<_d^VG$+zT-N==6RG{pI$bg>-h!Y z;~t?eEaYVZUg~4bF?*Sa>v6FDV|;Z*{5FYLARpXNN*TR5<>Wfg_gNg5p{<=}EbzWPv3xTTA5Q068Qu3Ica0a)rl+t=7POOWJP45D zcXeM6+G8Tc(yF#YroD-3+9GEvmkIG&v7E*49f;8!wBEuCtDRYT_UbB1=;@tT3${Mx z%OrA621)Wvu=`vIuVXPH*bI#QGPZN70zDdsl?}}7PWQXoDRhVl8TnIL<|n*1xG^er zxzv^)$!;f3S%p;%v(!dkSkzPEvwa=AJ&svwE;KLZ?II{*Lx diff --git a/papers/Collabra/paper.tex b/papers/Collabra/paper.tex index 350172f23..492f8fa85 100644 --- a/papers/Collabra/paper.tex +++ b/papers/Collabra/paper.tex @@ -116,7 +116,7 @@ regarding the diagnosis and treatment of outliers, an additional difficulty arises concerning the mathematical implementation of the recommended methods. In this paper, we provide an overview of current -recommandations and best practices and demonstrate how they can easily +recommendations and best practices and demonstrate how they can easily and conveniently be implemented in the R statistical computing software, using the \emph{\{performance\}} package of the \emph{easystats} ecosystem. We cover univariate, multivariate, and model-based @@ -140,7 +140,7 @@ \section{Introduction}\label{introduction}} it---be it because they belong to a different distribution (originating from a different generative process) or simply being extreme cases, statistically rare but not impossible---can be hard to assess, and the -boundaries of ``abnormal'' are hard to define. +boundaries of ``abnormal'' difficult to define. Nonetheless, the improper handling of these outliers can substantially affect statistical model estimations, biasing effect estimations and @@ -148,16 +148,16 @@ \section{Introduction}\label{introduction}} address this problem in a thoughtful manner. Yet, despite the existence of established recommendations and guidelines, many researchers still do not treat outliers in a consistent manner, or do so using inappropriate -strategies (Simmons, Nelson, and Simonsohn 2011; Leys et al. 2013). +strategies (Leys et al., 2013; Simmons et al., 2011). One possible reason is that researchers are not aware of the existing recommendations, or do not know how to implement them using their analysis software. In this paper, we show how to follow current best practices for automatic and reproducible statistical outlier detection -(SOD) using R and the \emph{\{performance\}} package (Lüdecke et al. +(SOD) using R and the \emph{\{performance\}} package (Lüdecke et al., 2021), which is part of the \emph{easystats} ecosystem of packages that build an R framework for easy statistical modeling, visualization, and -reporting (Lüdecke et al. 2022). +reporting (Lüdecke et al., 2019/2023). \hypertarget{identifying-outliers}{% \section{Identifying Outliers}\label{identifying-outliers}} @@ -168,7 +168,7 @@ \section{Identifying Outliers}\label{identifying-outliers}} influence of outliers and they assume normally distributed data (i.e., a Gaussian distribution). Therefore, current guidelines recommend using robust methods to identify outliers, such as those relying on the median -as opposed to the mean (Leys et al. 2019, 2013, 2018). +as opposed to the mean (Leys et al., 2013, 2018, 2019). Nonetheless, which exact outlier method to use depends on many factors. In some cases, eye-gauging odd observations can be an appropriate @@ -200,7 +200,7 @@ \section{Identifying Outliers}\label{identifying-outliers}} Importantly, whatever approach researchers choose remains a subjective decision, which usage (and rationale) must be transparently documented -and reproducible (Leys et al. 2019). Researchers should commit (ideally +and reproducible (Leys et al., 2019). Researchers should commit (ideally in a preregistration) to an outlier treatment method before collecting the data. They should report in the paper their decisions and details of their methods, as well as any deviation from their original plan. These @@ -219,8 +219,8 @@ \subsection{Univariate Outliers}\label{univariate-outliers}} as mentioned earlier, this popular method is not robust. Therefore, for univariate outliers, it is recommended to use the median along with the Median Absolute Deviation (MAD), which are more robust than the -interquartile range or the mean and its standard deviation (Leys et al. -2019, 2013). +interquartile range or the mean and its standard deviation (Leys et al., +2013, 2019). Researchers can identify outliers based on robust (i.e., MAD-based) \emph{z} scores using the \texttt{check\_outliers()} function of the @@ -328,7 +328,7 @@ \subsection{Multivariate Outliers}\label{multivariate-outliers}} variable, for instance the reaction time, as extreme values might be indicative of inattention or non-task-related behavior\footnote{ Note that they might not be the optimal way of treating reaction time - outliers (Ratcliff 1993; Van Zandt and Ratcliff 1995)}. + outliers (Ratcliff, 1993; Van Zandt \& Ratcliff, 1995)}. However, in many scenarios, variables of a data set are not independent, and an abnormal observation will impact multiple dimensions. For @@ -343,7 +343,7 @@ \subsection{Multivariate Outliers}\label{multivariate-outliers}} robust and is heavily influenced by the outliers themselves. Therefore, for multivariate outliers, it is recommended to use the Minimum Covariance Determinant, a robust version of the Mahalanobis distance -(MCD, Leys et al. 2018, 2019). +(MCD, Leys et al., 2018, 2019). In \emph{\{performance\}}'s \texttt{check\_outliers()}, one can use this approach with \texttt{method\ =\ "mcd"}.\footnote{Our default threshold @@ -377,7 +377,7 @@ \subsection{Multivariate Outliers}\label{multivariate-outliers}} Other multivariate methods are available, such as another type of robust Mahalanobis distance that in this case relies on an orthogonalized -Gnanadesikan-Kettenring pairwise estimator (Gnanadesikan and Kettenring +Gnanadesikan-Kettenring pairwise estimator (Gnanadesikan \& Kettenring, 1972). These methods are documented and described in the function's \href{https://easystats.github.io/performance/reference/check_outliers.html}{help page}. @@ -470,16 +470,17 @@ \subsection{Model-Based Outliers}\label{model-based-outliers}} \end{longtable} \hypertarget{cooks-distance-vs.-mcd}{% -\subsubsection{Cook's Distance vs.~MCD}\label{cooks-distance-vs.-mcd}} +\subsection{Cook's Distance vs.~MCD}\label{cooks-distance-vs.-mcd}} Leys et al. (2018) report a preference for the MCD method over Cook's distance. This is because Cook's distance removes one observation at a -time and checks its corresponding influence on the model each time (Cook -1977), and flags any observation that has a large influence. In the view -of these authors, when there are several outliers, the process of -removing a single outlier at a time is problematic as the model remains -``contaminated'' or influenced by other possible outliers in the model, -rendering this method suboptimal in the presence of multiple outliers. +time and checks its corresponding influence on the model each time +(Cook, 1977), and flags any observation that has a large influence. In +the view of these authors, when there are several outliers, the process +of removing a single outlier at a time is problematic as the model +remains ``contaminated'' or influenced by other possible outliers in the +model, rendering this method suboptimal in the presence of multiple +outliers. However, distribution-based approaches are not a silver bullet either, and there are cases where the usage of methods agnostic to theoretical @@ -561,15 +562,16 @@ \subsubsection{Cook's Distance vs.~MCD}\label{cooks-distance-vs.-mcd}} outliers is a significant concern, regression methods that are more robust to outliers should be considered---like \emph{t} regression or quantile regression---as they render their precise identification less -critical (McElreath 2020). +critical (McElreath, 2020). -\hypertarget{multiple-methods}{% -\subsection{Multiple Methods}\label{multiple-methods}} +\hypertarget{composite-outlier-score}{% +\subsection{Composite Outlier Score}\label{composite-outlier-score}} -An alternative approach that is possible is to combine several methods, -based on the assumption that different methods provide different angles -of looking at the problem. By applying a variety of methods, one can -hope to ``triangulate'' the true outliers (those consistently flagged by +The \emph{\{performance\}} package also offers an alternative, +consensus-based approach that combines several methods, based on the +assumption that different methods provide different angles of looking at +a given problem. By applying a variety of methods, one can hope to +``triangulate'' the true outliers (those consistently flagged by multiple methods) and thus attempt to minimize false positives. In practice, this approach computes a composite outlier score, formed of @@ -619,13 +621,12 @@ \subsection{Multiple Methods}\label{multiple-methods}} \begin{quote} Based on a composite outlier score (see the `check\_outliers()' function -in the `performance' R package, (Lüdecke et al. 2021)) obtained via the +in the `performance' R package, Lüdecke et al., 2021) obtained via the joint application of multiple outliers detection algorithms ((a) median -absolute deviation (MAD)-based robust \emph{z} scores, (Leys et al. -2013); (b) Mahalanobis minimum covariance determinant (MCD), (Leys et -al. 2019); and (c) Cook's distance, (Cook 1977)), we excluded two -participants that were classified as outliers by at least half of the -methods used. +absolute deviation (MAD)-based robust \emph{z} scores, Leys et al., +2013; (b) Mahalanobis minimum covariance determinant (MCD), Leys et al., +2019; and (c) Cook's distance, Cook, 1977), we excluded two participants +that were classified as outliers by at least half of the methods used. \end{quote} \hypertarget{handling-outliers}{% @@ -664,10 +665,11 @@ \subsection{Error, Interesting, and Random It is recommended to \emph{keep} observations which are expected to be part of the distribution of interest, even if they are outliers (Leys et -al. 2019). However, if it is suspected that the outliers belong to an +al., 2019). However, if it is suspected that the outliers belong to an alternative distribution, then those observations could have a large impact on the results and call into question their robustness, -especially if significance is conditional on their inclusion. +especially if significance is conditional on their inclusion, so should +be removed. On the other hand, there are also outliers that cannot be detected by statistical tools, but should be found and removed. For example, if we @@ -684,15 +686,15 @@ \subsection{Winsorization}\label{winsorization}} extent of their impact on results. This approach however can reduce statistical power. Therefore, some propose a \emph{recoding} approach, namely, winsorization: bringing outliers back within acceptable limits -(e.g., 3 MADs, Tukey and McLaughlin 1963). However, if possible, it is +(e.g., 3 MADs, Tukey \& McLaughlin, 1963). However, if possible, it is recommended to collect enough data so that even after removing outliers, there is still sufficient statistical power without having to resort to -winsorization (Leys et al. 2019). +winsorization (Leys et al., 2019). The \emph{easystats} ecosystem makes it easy to incorporate this step into your workflow through the \texttt{winsorize()} function of \emph{\{datawizard\}}, a lightweight R package to facilitate data -wrangling and statistical transformations (Patil et al. 2022). This +wrangling and statistical transformations (Patil et al., 2022). This procedure will bring back univariate outliers within the limits of `acceptable' values, based either on the percentile, the \emph{z} score, or its robust alternative based on the MAD. @@ -735,17 +737,17 @@ \subsection{The Importance of reproducible manner. Ideally, the handling of outliers should be specified \emph{a priori} with as much detail as possible, and preregistered, to limit researchers' degrees of freedom and therefore -risks of false positives (Leys et al. 2019). This is especially true +risks of false positives (Leys et al., 2019). This is especially true given that interesting outliers and random outliers are often times hard to distinguish in practice. Thus, researchers should always prioritize transparency and report all of the following information: (a) how many -outliers were identified; (b) according to which method and criteria, -(c) using which function of which R package (if applicable), and (d) how -they were handled (excluded or winsorized, if the latter, using what -threshold). If at all possible, (e) the corresponding code script along -with the data should be shared on a public repository like the Open -Science Framework (OSF), so that the exclusion criteria can be -reproduced precisely. +outliers were identified (including percentage); (b) according to which +method and criteria, (c) using which function of which R package (if +applicable), and (d) how they were handled (excluded or winsorized, if +the latter, using what threshold). If at all possible, (e) the +corresponding code script along with the data should be shared on a +public repository like the Open Science Framework (OSF), so that the +exclusion criteria can be reproduced precisely. \hypertarget{conclusion}{% \section{Conclusion}\label{conclusion}} @@ -763,6 +765,31 @@ \section{Conclusion}\label{conclusion}} research practices while providing a smooth outlier detection experience. +\hypertarget{contributions}{% +\subsubsection{Contributions}\label{contributions}} + +Author 1 drafted the paper; all authors contributed to both the writing +of the paper and the conception of the software. + +\hypertarget{acknowledgements}{% +\subsubsection{Acknowledgements}\label{acknowledgements}} + +\emph{\{performance\}} is part of the collaborative +\href{https://github.com/easystats/easystats}{\emph{easystats}} +ecosystem (Lüdecke et al., 2019/2023). Thus, we thank all +\href{https://github.com/orgs/easystats/people}{members of easystats}, +contributors, and users alike. + +\hypertarget{funding-information}{% +\subsubsection{Funding information}\label{funding-information}} + +This research received no external funding. + +\hypertarget{competing-interests}{% +\subsubsection{Competing Interests}\label{competing-interests}} + +The authors declare no conflict of interest + \hypertarget{references}{% \section*{References}\label{references}} \addcontentsline{toc}{section}{References} @@ -770,84 +797,81 @@ \section*{References}\label{references}} \hypertarget{refs}{} \begin{CSLReferences}{1}{0} \leavevmode\vadjust pre{\hypertarget{ref-cook1977detection}{}}% -Cook, R. Dennis. 1977. {``Detection of Influential Observation in Linear -Regression.''} \emph{Technometrics} 19 (1): 15--18. -\url{https://doi.org/10.1080/00401706.1977.10489493}. +Cook, R. D. (1977). 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GIT binary patch delta 47 wcmeyM{y}|$xr(8=p}DD{k*Ow^zHfetOJYf?f`*Hgk%5u1feB1*WAs#E07@tf`2YX_ delta 47 wcmeyM{y}|$xr%|2p{c34sf8w&zHfetOJYf?f`*Hgk%5u1feB1*WAs#E07`@n0RR91 diff --git a/papers/Collabra/paper_files/figure-latex/scatter-1.pdf b/papers/Collabra/paper_files/figure-latex/scatter-1.pdf index bbf1beaf88944d13ac695cd3f267b9f70f925356..b090ab565b118b9d5b5ae008d02221fcbf89ec7e 100644 GIT binary patch delta 47 wcmZ2uv&LqExr(8=p}DD{k+~+9zHfetOJYf?f`*Hgk%5u1feB1*WAsH?06FLk Less convinced as a scientific research is the major concern. I cannot find a solid contribution for the statistical methodologies, new packages, or sound applications in this study. Almost all the obtained conclusions are known. The readers would be happy to see more convincing results from good real examples from the real world if only the well known statistical methods and packages are used in this study. The tutorial-like results using the examples in R are too weak for an academic paper. It is contributive if the authors can include real examples in different areas to show the power of the used package and present the insight findings, not just show how to use the packages. Then, resubmit the revision as a new paper for review. + +First, we thank the *Mathematics* Editor for their analysis of the paper. We agree that the paper was perhaps less suited to a purely mathematical journal and more so for psychology-oriented journals encouraging open science, good research practices, and good statistical practices. As for the contributions, we believe we make a unique contribution through our proposal of a consensus-based approach to detecting outliers, as well as through our argument that researchers should prefer model-based outlier detection methods over, for example, the Minimum Covariance Determinant (MCD) method which is currently recommended in other guideline documents. We have thus expanded this section to make the contribution more substantial in the revised version of the manuscript, and, as suggested by the Editor, added a real-world example further illustrating our point. + +# Reviewer 1 comments: + +> In this paper, the authors have shown how to search for outliers using the check_outliers() function of the {performance} package while following current good practices. This contribution will help researchers engage in good search practices while providing an outlier detection experience. They cover univariate, multivariate, and model-based statistical outlier detection methods, their recommended threshold, standard output, and plotting methods. The present paper represents the subject of check the outliers, An accessible introduction to identifying statistical outliers in R with easystats. The study design and methods appropriate for the research question. The results presented clearly and accurately. The authors logically explain the findings. I highly recommend the publication of this paper in Mathematics Journal. + +Overall, this reviewer has very positive comments, requests no additional changes, and highly recommend the paper for publication. + +# Reviewer 2 comments: + +> The authors propose the illustration of an R library for detecting outliers. The paper is quite clear, however, the following remarks are provided to improve the article + +> - The word accessible in the title should be removed. + +This has been fixed. + +> - The authors should clarify whether the functions implemented in the library were implemented only for continuous variables or other types of variables are also considered. + +This has been fixed. + +> - The author's reference to the Normal distribution on page 2, line 31 is unclear. They should clarify or delete this sentence. + +This has been fixed. + +> - The reference to the mathematical score is unclear on page 2, line 36. I think this reference should be removed. + +This has been fixed. + +> A critical review on the analysis of outliers is proposed in this article which must be cited + +> Riani, M., & Atkinson, A. C. (2020). Robust regression methods in machine learning. Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery, 10(2), e1359. + +Thank you for this suggestion. We have added a reference to robust regression methods, although we have opted for a different, more suited reference. + +> - Page 3, lines 101-102: It is unclear what the authors mean when referring to BCA, a technique used in non-parametric bootstrapping, but the paper does not mention this. + +At the end of the univariate outliers section, we mention that other methods (in addition to robust *z* scores) are available, and give a few examples, including of the Bias Corrected and Accelerated Interval. Given that we mention that these methods are documented and described in the corresponding functions’ help pages, we think it would not be appropriate to provide an in-depth explanation of these concepts in the current paper since the topic is too tangential to the paper's objectives. + +> - It is necessary to change the x-axis labels of all the figures as the numbers overlap; they should be written in a smaller font or otherwise eliminate some of them since they are not readable. I am talking about the figures referring to the histogram of the outliers. + +This has been fixed. + +> - Page seven, line 146, it is better to write association instead of relationship. + +This has been fixed. + +> - Page 7, line 154, the authors should specify what they mean by compatible regression models. + +This has been fixed. + +> - Page 7, code of the first chunk, the authors use the iqr method, but this is not discussed above. They must add details of all the methods they show in the output. + +This has been fixed. + +> - Page 9, line 247, it is difficult to follow the discussion for those unfamiliar with the R datawizard package. What does it do? How does the proposed function tie in with those in the package? + +This has been fixed. + +> - Page 10, line 272, what does " Registration " mean? + +The word in question was "preregistration", and we think that for a journal such as *Collabra: Psychology*, the readers will be familiar enough with this common concept that there is no need to define it. + +> - Check the reference style because it is not uniform + +We now use APA style. + +# Reviewer 3 comments: + +> The paper outlines techniques for processing data with inhomogeneities, such as outliers. However, the style of the article does not correspond to scientific research. The work is educational and auxiliary in nature and is more in line with educational publications, including popular scientific ones. + +We respectfully disagree with this comment. Good research practices as well as good statistical practices are of paramount importance in this era of the replication crisis, especially in psychology. However, having scattered specialized works covering some of these aspects is not enough for the common, non-expert psychologists. There must also be accessible works that not only gives a cohesive and comprehensive overview of the issues, but also show how to easily apply these guidelines in practice in their own research. We believe we thus make an important applied contribution for psychologists in this regard. + +In addition, we also make a unique theoretical contribution through our proposal of a consensus-based approach to detecting outliers, as well as through our argument that researchers should prefer model-based outlier detection methods over, for example, the Minimum Covariance Determinant (MCD) method which is currently recommended in other guideline documents. 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<13123390+rempsyc@users.noreply.github.com> Date: Sat, 13 May 2023 17:03:52 -0400 Subject: [PATCH 07/34] JOSE folder [skip ci] --- papers/JOSE/apa.csl | 1917 +++++++++++++++++ papers/JOSE/arxiv.sty | 255 +++ papers/JOSE/cover_letter.Rmd | 29 + papers/JOSE/cover_letter.pdf | Bin 0 -> 56483 bytes papers/JOSE/mybibfile.bib | 161 ++ papers/JOSE/paper.Rmd | 347 +++ papers/JOSE/paper.log | 1479 +++++++++++++ papers/JOSE/paper.md | 429 ++++ papers/JOSE/paper.pdf | Bin 0 -> 234058 bytes papers/JOSE/paper_files/Editor comments.pdf | Bin 0 -> 190532 bytes papers/JOSE/paper_files/Editor email.pdf | Bin 0 -> 480178 bytes .../JOSE/paper_files/Reviewer 1 comments.pdf | Bin 0 -> 168997 bytes .../JOSE/paper_files/Reviewer 2 comments.pdf | Bin 0 -> 182989 bytes .../JOSE/paper_files/Reviewer 3 comments.pdf | Bin 0 -> 167380 bytes papers/JOSE/paper_files/Reviewer comments.pdf | Bin 0 -> 423076 bytes .../paper_files/Reviewer comments_short.pdf | Bin 0 -> 374787 bytes papers/JOSE/paper_files/Tite page.pdf 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papers/JOSE/paper_files/figure-latex/multimethod-1.pdf create mode 100644 papers/JOSE/paper_files/figure-latex/multivariate-1.pdf create mode 100644 papers/JOSE/paper_files/figure-latex/multivariate_implicit-1.pdf create mode 100644 papers/JOSE/paper_files/figure-latex/scatter-1.pdf create mode 100644 papers/JOSE/paper_files/figure-latex/univariate-1.pdf create mode 100644 papers/JOSE/paper_files/figure-latex/univariate_implicit-1.pdf create mode 100644 papers/JOSE/paper_files/figure-latex/unnamed-chunk-3-1.pdf create mode 100644 papers/JOSE/paper_files/figure-latex/unnamed-chunk-4-1.pdf create mode 100644 papers/JOSE/paper_files/figure-latex/unnamed-chunk-5-1.pdf create mode 100644 papers/JOSE/paper_files/figure-latex/unnamed-chunk-5-2.pdf create mode 100644 papers/JOSE/reviewer_response.Rmd create mode 100644 papers/JOSE/reviewer_response.pdf diff --git a/papers/JOSE/apa.csl b/papers/JOSE/apa.csl new file mode 100644 index 000000000..946c7fcd2 --- /dev/null +++ b/papers/JOSE/apa.csl 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rules for title box at top of first page +\newcommand{\@toptitlebar}{ + \hrule height 2\p@ + \vskip 0.25in + \vskip -\parskip% +} +\newcommand{\@bottomtitlebar}{ + \vskip 0.29in + \vskip -\parskip + \hrule height 2\p@ + \vskip 0.09in% +} + +% create title (includes both anonymized and non-anonymized versions) +\providecommand{\@maketitle}{} +\renewcommand{\@maketitle}{% + \vbox{% + \hsize\textwidth + \linewidth\hsize + \vskip 0.1in + \@toptitlebar + \centering + {\LARGE\sc \@title\par} + \@bottomtitlebar + \textsc{A Preprint}\\ + \vskip 0.1in + \def\And{% + \end{tabular}\hfil\linebreak[0]\hfil% + \begin{tabular}[t]{c}\bf\rule{\z@}{24\p@}\ignorespaces% + } + \def\AND{% + \end{tabular}\hfil\linebreak[4]\hfil% + \begin{tabular}[t]{c}\bf\rule{\z@}{24\p@}\ignorespaces% + } + \begin{tabular}[t]{c}\bf\rule{\z@}{24\p@}\@author\end{tabular}% + \vskip 0.4in \@minus 0.1in \center{\today} \vskip 0.2in + } +} + +% add conference notice to bottom of first page +\newcommand{\ftype@noticebox}{8} +\newcommand{\@notice}{% + % give a bit of extra room back to authors on first page + \enlargethispage{2\baselineskip}% + \@float{noticebox}[b]% + \footnotesize\@noticestring% + \end@float% +} + +% abstract styling +\renewenvironment{abstract} +{ + \centerline + {\large \bfseries \scshape Abstract} + \begin{quote} +} +{ + \end{quote} +} + +\endinput diff --git a/papers/JOSE/cover_letter.Rmd b/papers/JOSE/cover_letter.Rmd new file mode 100644 index 000000000..4251c050a --- /dev/null +++ b/papers/JOSE/cover_letter.Rmd @@ -0,0 +1,29 @@ +--- +output: pdf_document +--- + +Dear Dr. Vazire, + +We are pleased to submit this paper to *Collabra: Psychology*. + +The paper, titled "Check your outliers! An introduction to identifying statistical outliers in R with *easystats*", provides an overview of current recommendations and best practices regarding the diagnosis and treatment of outliers, a common issue faced by researchers---and a potential source of scientific malpractice. + +It explains the key approaches, highlights recommendations, and shows how users can adopt them in their R analysis with a single function. The manuscript covers univariate, multivariate, and model-based statistical outlier detection methods, their recommended threshold, standard output, and plotting method, among other things. + +Beyond acting like a concise review of outlier treatment procedures and practical tutorial, we also introduce a new outlier-detection method that relies on a consensus-based approach. In this sense, the paper fits well with the "Methodology and Research Practice in Psychology" section of the journal, as it essentially communicates to psychologists how to easily follow some of the best practices in the detection of statistical outlier using currently available open source and free software. This makes the manuscript relevant to data science, behavioural science, and good research and statistical practices more generally. + +As Associated Editor, we would like to suggest Jeffrey Girard, as he is familiar with the *easystats* and R ecosystems, as well as good statistical practices. Additionally, we would like to request a streamlined review, as the manuscript has been rejected within the previous 365 days from the journal *Mathematics*. Accordingly, we provide in this submission a detailed letter that includes prior reviews, the decision letter, as well as how we addressed the reviewers' comments. We have in this regard integrated most of the changes suggested by the reviewers. Note that the previous editors and reviewers have not given their permission for their comments to be openly available at *Collabra: Psychology*. However, although an open review was requested, the reviewers did not sign their reviews. + +Our current submission is original and has been neither published elsewhere nor is currently under consideration for publication elsewhere. All authors have contributed substantially to the software and manuscript. All authors gave final approval to the manuscript and accept to be accountable. We have no conflicts of interest to disclose. We have also read the Transparency and Openness policy of the Editorial Policies of *Collabra: Psychology*. + +Thank you for considering our submission. + +On the behalf of all authors, + +Rémi Thériault + +Department of Psychology, + +Université du Québec à Montréal, + +Montréal, Québec, Canada \ No newline at end of file diff --git a/papers/JOSE/cover_letter.pdf b/papers/JOSE/cover_letter.pdf new file mode 100644 index 0000000000000000000000000000000000000000..15650f828a5911b0fdaa1526bfab944c863573a8 GIT binary patch literal 56483 zcma&M19T=`(=Hs_m`tq6#I|kQ6Wg{Yb~3ST+qNgRZA^@lnauOO&v)McU+eT*UH9(l zs@ip3Ro&U$X(AZ`Axc^*Mku1mnZ5-mT09y&D_v744h}qOc|2-iD+Mb&Y5_cTx_7-C z9<`8(y(S(P7nFge{%)0Cz80cB) z8$i7~+u7S1=vY8GFZrvA$F4NOwx3rVq-K{V%YHfHC1tK?TRc&6IdzcS;!gz@-l}a> z633Rk%Dp}YM##iDO+WPGL<02%fpEX?jBpIptbKY2JlHyqgy(+VwGyo+@1a9`INLNK z?vv`5{Y+$gCv*Oa+B$8zuud$B)QZXHF5>5P7Rn&=M(@|Y{Pwgtzv_WvC|lJMX`u4e zH{W9oO*GRa8{>X+#?-(;l3GuC>Exy{(k}=7(7`;+z{Fu`J(OUwhXYW_?{u%^w4V;r 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zz3@+aQne0kvS<;xyGu6r{HENQ1mUXrw+tYwQ1hjbAr&~5p|JLVW!-U2Hc-b+(4)U^P*t_?X-aHcX;edx|WDwvP zE0iUqTsHBjdzscnMo<>~)Hu2wgi_ zX5lJBDeHGJOw)Jlp7MHPF8?E$(8&CE#pTMx!z(O@wz|ZhWv<0%T!*f#+Y>!AbclD8 zXlvxPC-j-EPl7$a=G~e;crr7sZc1*pJZ&yAV8hb_`q~#)9cB4DbkLQ%(>h#zVt#L} zv>tq5FLLkU1!Oj5ExD;)lHFSRK1Uv&bq4v-NtxX3uv-J;(9Jio4gP#pu>&93xo%(O zXC?4kOefcQ-N*FmZWt_6N=?dSCujS z8R!bNIx8ogybN@*O$+ryj(w7<Xp1kaC^wgmdY5zkbmkHqA z+-~%^^@#M&yBv1gU5-d+2FGBc!s!F(W=Vob@ZLeh6I*T6%cY($W+7(SUuB+!2?~9mQSmq8=_xUfUj+)zCn7I=>2NVGsDi^yUu< zGRb{wKM+{BIg?`K$#SE*bJuG`r?_j9SyWI&E~N2qqZbr+@r&aaGiVN;WZ>7Lw4bVP zMmY%49UQ@nDiVf4z)%=aPiuOzoM{XtWw;rYOyKD3=D~ZAt0s26e%w$lYJNzMESiW0XMR~677J4MQy&TiuJ+||C>-&pIir!_JK*v-1R9I^aa;uO4EphS zXgreeiemK_Y)V9u|ut{Fqa4BJe-QVYr3P@^P`)rN?72 z?15zx16Wx>a8v3D3itfN571~VX#SoBH=&-pBMp3sn!lsrdODExZiJ2|9*fh$Xc37d xZG). + +## Multivariate Outliers + +Univariate outliers can be useful when the focus is on a particular variable, for instance the reaction time, as extreme values might be indicative of inattention or non-task-related behavior^[ Note that they might not be the optimal way of treating reaction time outliers [@ratcliff1993methods; @van1995statistical]]. + +However, in many scenarios, variables of a data set are not independent, and an abnormal observation will impact multiple dimensions. For instance, a participant giving random answers to a questionnaire. In this case, computing the _z_ score for each of the questions might not lead to satisfactory results. Instead, one might want to look at these variables together. + +One common approach for this is to compute multivariate distance metrics such as the Mahalanobis distance. Although the Mahalanobis distance is very popular, just like the regular _z_ scores method, it is not robust and is heavily influenced by the outliers themselves. Therefore, for multivariate outliers, it is recommended to use the Minimum Covariance Determinant, a robust version of the Mahalanobis distance [MCD, @leys2018outliers; @leys2019outliers]. + +In *{performance}*'s `check_outliers()`, one can use this approach with `method = "mcd"`.^[Our default threshold for the MCD method is defined by `stats::qchisq(p = 1 - 0.001, df = ncol(x))`, which again is an approximation of the critical value for _p_ < .001 consistent with the thresholds of our other methods.] + +```{r multivariate} +outliers <- check_outliers(data, method = "mcd") +outliers +``` + +```{r multivariate_plot, eval=FALSE} +plot(outliers) +``` + +```{r multivariate_implicit, fig.cap = "Visual depiction of outliers using the Minimum Covariance Determinant (MCD) method, a robust version of the Mahalanobis distance. The distance represents the MCD scores for variables mpg, cyl, disp, and hp.", echo=FALSE} +plot(outliers) + + ggplot2::theme(axis.text.x = ggplot2::element_text( + angle = 45, size = 7 +)) +``` + +Other multivariate methods are available, such as another type of robust Mahalanobis distance that in this case relies on an orthogonalized Gnanadesikan-Kettenring pairwise estimator [@gnanadesikan1972robust]. These methods are documented and described in the function's [help page](https://easystats.github.io/performance/reference/check_outliers.html). + +## Model-Based Outliers + +Working with regression models creates the possibility of using model-based SOD methods. These methods rely on the concept of *leverage*, that is, how much influence a given observation can have on the model estimates. If few observations have a relatively strong leverage/influence on the model, one can suspect that the model's estimates are biased by these observations, in which case flagging them as outliers could prove helpful (see next section, "Handling Outliers"). + +In {performance}, two such model-based SOD methods are currently available: Cook's distance, for regular regression models, and Pareto, for Bayesian models. As such, `check_outliers()` can be applied directly on regression model objects, by simply specifying `method = "cook"` (or `method = "pareto"` for Bayesian models).^[Our default threshold for the Cook method is defined by `stats::qf(0.5, ncol(x), nrow(x) - ncol(x))`, which again is an approximation of the critical value for _p_ < .001 consistent with the thresholds of our other methods.] + +```{r model, fig.cap = "Visual depiction of outliers based on Cook's distance (leverage and standardized residuals), based on the fitted model."} +model <- lm(disp ~ mpg * disp, data = data) +outliers <- check_outliers(model, method = "cook") +outliers + +plot(outliers) +``` + +Table 1 below summarizes which methods to use in which cases, and with what threshold. + +```{r, echo=FALSE} +df <- data.frame( + `Statistical Test` = c( + "Supported regression model", + "Structural Equation Modeling (or other unsupported model)", + "Simple test with few variables (*t* test, correlation, etc.)"), + `Diagnosis Method` = c( + "**Model-based**: Cook (or Pareto for Bayesian models)", + "**Multivariate**: Minimum Covariance Determinant (MCD)", + "**Univariate**: robust *z* scores (MAD)"), + `Recommended Threshold` = c( + "`qf(0.5, ncol(x), nrow(x) - ncol(x))` (or 0.7 for Pareto)", + "`qchisq(p = 1 - 0.001, df = ncol(x))`", + "`qnorm(p = 1 - 0.001 / 2)`, ~ 3.29") +) +knitr::kable( + df, col.names = gsub("[.]", " ", names(df)), + caption = "Summary of Statistical Outlier Detection Methods Recommendations.", longtable = TRUE) +``` + +## Cook's Distance vs. MCD + +@leys2018outliers report a preference for the MCD method over Cook's distance. This is because Cook's distance removes one observation at a time and checks its corresponding influence on the model each time [@cook1977detection], and flags any observation that has a large influence. In the view of these authors, when there are several outliers, the process of removing a single outlier at a time is problematic as the model remains "contaminated" or influenced by other possible outliers in the model, rendering this method suboptimal in the presence of multiple outliers. + +However, distribution-based approaches are not a silver bullet either, and there are cases where the usage of methods agnostic to theoretical and statistical models of interest might be problematic. For example, a very tall person would be expected to also be much heavier than average, but that would still fit with the expected association between height and weight (i.e., it would be in line with a model such as `weight ~ height`). In contrast, using multivariate outlier detection methods there may flag this person as being an outlier---being unusual on two variables, height and weight---even though the pattern fits perfectly with our predictions. + +In the example below, we plot the raw data and see two possible outliers. The first one falls along the regression line, and is therefore "in line" with our hypothesis. The second one clearly diverges from the regression line, and therefore we can conclude that this outlier may have a disproportionate influence on our model. + +```{r scatter, fig.cap = "Scatter plot of height and weight, with two extreme observations: one model-consistent (top-right) and the other, model-inconsistent (i.e., an outlier; bottom-right)."} +data <- women[rep(seq_len(nrow(women)), each = 100), ] +data <- rbind(data, c(100, 258), c(100, 200)) +model <- lm(weight ~ height, data) +rempsyc::nice_scatter(data, "height", "weight") +``` + +Using either the *z*-score or MCD methods, our model-consistent observation will be incorrectly flagged as an outlier or influential observation. + +```{r} +outliers <- check_outliers(model, method = c("zscore_robust", "mcd")) +which(outliers) +``` + +In contrast, the model-based detection method displays the desired behaviour: it correctly flags the person who is very tall but very light, without flagging the person who is both tall and heavy. + +```{r model2, fig.cap = "The leverage method (Cook's distance) correctly distinguishes the true outlier from the model-consistent extreme observation), based on the fitted model."} +outliers <- check_outliers(model, method = "cook") +which(outliers) +plot(outliers) +``` + +Finally, unusual observations happen naturally: extreme observations are expected even when taken from a normal distribution. While statistical models can integrate this "expectation", multivariate outlier methods might be too conservative, flagging too many observations despite belonging to the right generative process. For these reasons, we believe that model-based methods are still preferable to the MCD when using supported regression models. Additionally, if the presence of multiple outliers is a significant concern, regression methods that are more robust to outliers should be considered---like _t_ regression or quantile regression---as they render their precise identification less critical [@mcelreath2020statistical]. + +## Composite Outlier Score + +The *{performance}* package also offers an alternative, consensus-based approach that combines several methods, based on the assumption that different methods provide different angles of looking at a given problem. By applying a variety of methods, one can hope to "triangulate" the true outliers (those consistently flagged by multiple methods) and thus attempt to minimize false positives. + +In practice, this approach computes a composite outlier score, formed of the average of the binary (0 or 1) classification results of each method. It represents the probability that each observation is classified as an outlier by at least one method. The default decision rule classifies rows with composite outlier scores superior or equal to 0.5 as outlier observations (i.e., that were classified as outliers by at least half of the methods). In *{performance}*'s `check_outliers()`, one can use this approach by including all desired methods in the corresponding argument. + +```{r multimethod, fig.cap = "Visual depiction of outliers using several different statistical outlier detection methods."} +outliers <- check_outliers(model, method = c("zscore_robust", "mcd", "cook")) +which(outliers) +``` + +Outliers (counts or per variables) for individual methods can then be obtained through attributes. For example: + +```{r} +attributes(outliers)$outlier_var$zscore_robust +``` + +An example sentence for reporting the usage of the composite method could be: + +> Based on a composite outlier score [see the 'check_outliers()' function in the 'performance' R package, @ludecke2021performance] obtained via the joint application of multiple outliers detection algorithms [(a) median absolute deviation (MAD)-based robust _z_ scores, @leys2013outliers; (b) Mahalanobis minimum covariance determinant (MCD), @leys2019outliers; and (c) Cook's distance, @cook1977detection], we excluded two participants that were classified as outliers by at least half of the methods used. + +# Handling Outliers + +The above section demonstrated how to identify outliers using the `check_outliers()` function in the *{performance}* package. But what should we do with these outliers once identified? Although it is common to automatically discard any observation that has been marked as "an outlier" as if it might infect the rest of the data with its statistical ailment, we believe that the use of SOD methods is but one step in the get-to-know-your-data pipeline; a researcher or analyst's _domain knowledge_ must be involved in the decision of how to deal with observations marked as outliers by means of SOD. Indeed, automatic tools can help detect outliers, but they are nowhere near perfect. Although they can be useful to flag suspect data, they can have misses and false alarms, and they cannot replace human eyes and proper vigilance from the researcher. If you do end up manually inspecting your data for outliers, it can be helpful to think of outliers as belonging to different types of outliers, or categories, which can help decide what to do with a given outlier. + +## Error, Interesting, and Random Outliers + +@leys2019outliers distinguish between error outliers, interesting outliers, and random outliers. _Error outliers_ are likely due to human error and should be corrected before data analysis or outright removed since they are invalid observations. _Interesting outliers_ are not due to technical error and may be of theoretical interest; it might thus be relevant to investigate them further even though they should be removed from the current analysis of interest. _Random outliers_ are assumed to be due to chance alone and to belong to the correct distribution and, therefore, should be retained. + +It is recommended to _keep_ observations which are expected to be part of the distribution of interest, even if they are outliers [@leys2019outliers]. However, if it is suspected that the outliers belong to an alternative distribution, then those observations could have a large impact on the results and call into question their robustness, especially if significance is conditional on their inclusion, so should be removed. + +On the other hand, there are also outliers that cannot be detected by statistical tools, but should be found and removed. For example, if we are studying the effects of X on Y among teenagers and we have one observation from a 20-year-old, this observation might not be a _statistical outlier_, but it is an outlier in the _context_ of our research, and should be discarded to allow for valid inferences. + +## Winsorization + +_Removing_ outliers can in this case be a valid strategy, and ideally one would report results with and without outliers to see the extent of their impact on results. This approach however can reduce statistical power. Therefore, some propose a _recoding_ approach, namely, winsorization: bringing outliers back within acceptable limits [e.g., 3 MADs, @tukey1963less]. However, if possible, it is recommended to collect enough data so that even after removing outliers, there is still sufficient statistical power without having to resort to winsorization [@leys2019outliers]. + +The _easystats_ ecosystem makes it easy to incorporate this step into your workflow through the `winsorize()` function of *{datawizard}*, a lightweight R package to facilitate data wrangling and statistical transformations [@patil2022datawizard]. This procedure will bring back univariate outliers within the limits of 'acceptable' values, based either on the percentile, the _z_ score, or its robust alternative based on the MAD. + +```{r winsorization} +data[1501:1502, ] # See outliers rows + +# Winsorizing using the MAD +library(datawizard) +winsorized_data <- winsorize(data, method = "zscore", robust = TRUE, threshold = 3) + +# Values > +/- MAD have been winsorized +winsorized_data[1501:1502, ] +``` + +## The Importance of Transparency + +Once again, it is a critical part of a sound outlier treatment that regardless of which SOD method used, it should be reported in a reproducible manner. Ideally, the handling of outliers should be specified *a priori* with as much detail as possible, and preregistered, to limit researchers' degrees of freedom and therefore risks of false positives [@leys2019outliers]. This is especially true given that interesting outliers and random outliers are often times hard to distinguish in practice. Thus, researchers should always prioritize transparency and report all of the following information: (a) how many outliers were identified (including percentage); (b) according to which method and criteria, (c) using which function of which R package (if applicable), and (d) how they were handled (excluded or winsorized, if the latter, using what threshold). If at all possible, (e) the corresponding code script along with the data should be shared on a public repository like the Open Science Framework (OSF), so that the exclusion criteria can be reproduced precisely. + +# Conclusion + +In this paper, we have showed how to investigate outliers using the `check_outliers()` function of the *{performance}* package while following current good practices. However, best practice for outlier treatment does not stop at using appropriate statistical algorithms, but entails respecting existing recommendations, such as preregistration, reproducibility, consistency, transparency, and justification. Ideally, one would additionally also report the package, function, and threshold used (linking to the full code when possible). We hope that this paper and the accompanying `check_outlier()` function of *easystats* will help researchers engage in good research practices while providing a smooth outlier detection experience. + +### Contributions + +R.T. drafted the paper; all authors contributed to both the writing of the paper and the conception of the software. + +### Acknowledgements + +*{performance}* is part of the collaborative [*easystats*](https://github.com/easystats/easystats) ecosystem [@easystatspackage]. Thus, we thank all [members of easystats](https://github.com/orgs/easystats/people), contributors, and users alike. + +### Funding information + +This research received no external funding. + +### Competing Interests + +The authors declare no conflict of interest + +# References \ No newline at end of file diff --git a/papers/JOSE/paper.log b/papers/JOSE/paper.log new file mode 100644 index 000000000..02addf851 --- /dev/null +++ b/papers/JOSE/paper.log @@ -0,0 +1,1479 @@ +This is XeTeX, Version 3.141592653-2.6-0.999994 (MiKTeX 23.1) (preloaded format=xelatex 2023.2.25) 13 MAY 2023 16:49 +entering extended mode + restricted \write18 enabled. + %&-line parsing enabled. +**./paper.tex +(paper.tex +LaTeX2e <2022-11-01> patch level 1 +L3 programming layer <2023-02-02> (C:\Users\there\AppData\Local\Programs\MiKTeX +\tex/latex/base\article.cls +Document Class: article 2022/07/02 v1.4n Standard LaTeX document class +(C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/base\size10.clo +File: 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P., Nelson, L. D., & Simonsohn, U. (2011). False-p +ositive psy- + [] + + +Underfull \hbox (badness 3049) in paragraph at lines 1059--1065 +\TU/lmr/m/n/10 chology: Undisclosed flexibility in data collection and analysis + allows pre- + [] + + +Underfull \hbox (badness 3735) in paragraph at lines 1059--1065 +\TU/lmr/m/n/10 senting anything as significant. \TU/lmr/m/it/10 Psychological S +cience\TU/lmr/m/n/10 , \TU/lmr/m/it/10 22\TU/lmr/m/n/10 (11), 1359–1366. + [] + +File: C:/Users/there/AppData/Local/R/win-library/4.3/rticles/rmarkdown/template +s/joss/resources/JOSE-logo.png Graphic file (type bmp) + + +Package fancyhdr Warning: \headheight is too small (62.59596pt): +(fancyhdr) Make it at least 64.31554pt, for example: +(fancyhdr) \setlength{\headheight}{64.31554pt}. +(fancyhdr) You might also make \topmargin smaller to compensate: + +(fancyhdr) \addtolength{\topmargin}{-1.71957pt}. + +[12] (paper.aux) +Package rerunfilecheck Info: File `paper.out' has not changed. +(rerunfilecheck) Checksum: 8CE4AC14FC5D0DAC991EC18B63626103;2643. +Package logreq Info: Writing requests to 'paper.run.xml'. +\openout1 = `paper.run.xml'. + + ) +Here is how much of TeX's memory you used: + 37039 strings out of 411511 + 748993 string characters out of 5819115 + 1871001 words of memory out of 5000000 + 56702 multiletter control sequences out of 15000+600000 + 519215 words of font info for 87 fonts, out of 8000000 for 9000 + 1348 hyphenation exceptions out of 8191 + 84i,12n,81p,1196b,850s stack positions out of 10000i,1000n,20000p,200000b,200000s + +Output written on paper.pdf (12 pages). diff --git a/papers/JOSE/paper.md b/papers/JOSE/paper.md new file mode 100644 index 000000000..dafb1d9a5 --- /dev/null +++ b/papers/JOSE/paper.md @@ -0,0 +1,429 @@ +--- +title: "Check your outliers! An introduction to identifying statistical outliers in R with *easystats*" +authors: + - name: Rémi Thériault + orcid: 0000-0003-4315-6788 + affiliation: 1,* + - name: Mattan S. Ben-Shachar + orcid: 0000-0002-4287-4801 + affiliation: 2 + - name: Indrajeet Patil + orcid: 0000-0003-1995-6531 + affiliation: 3 + - name: Daniel Lüdecke + orcid: 0000-0002-8895-3206 + affiliation: 4 + - name: Brenton M. Wiernik + orcid: 0000-0001-9560-6336 + affiliation: 5 + - name: Dominique Makowski + orcid: 0000-0001-5375-9967 + affiliation: 6 +affiliations: + - index: 1 + name: Department of Psychology, Université du Québec à Montréal, Montréal, Québec, Canada + - index: 2 + name: Independent Researcher + - index: 3 + name: Center for Humans and Machines, Max Planck Institute for Human Development, Berlin, Germany + - index: 4 + name: Institute of Medical Sociology, University Medical Center Hamburg-Eppendorf, Germany + - index: 5 + name: Independent Researcher, Tampa, FL, USA + - index: 6 + name: School of Psychology, University of Sussex, Brighton, UK +correspondence: theriault.remi@courrier.uqam.ca. +type: article +status: submit +bibliography: mybibfile.bib +simplesummary: | + The *{performance}* package from the *easystats* ecosystem makes it easy to + diagnose outliers in R and according to current best practices thanks to the + `check_outiers()` function. +abstract: | + Beyond the challenge of keeping up-to-date with current best practices + regarding the diagnosis and treatment of outliers, an additional difficulty + arises concerning the mathematical implementation of the recommended methods. + In this paper, we provide an overview of current recommendations and best + practices and demonstrate how they can easily and conveniently be + implemented in the R statistical computing software, using the *{performance}* + package of the *easystats* ecosystem. We cover univariate, multivariate, and + model-based statistical outlier detection methods, their recommended + threshold, standard output, and plotting methods. We conclude with + recommendations on the handling of outliers: the different theoretical types + of outliers, whether to exclude or winsorize them, and the importance of + transparency. +keywords: | + univariate outliers; multivariate outliers; robust detection methods; R; easystats +acknowledgement: | + *{performance}* is part of the collaborative + [*easystats*](https://github.com/easystats/easystats) ecosystem + [@easystatspackage]. Thus, we thank all + [members of easystats](https://github.com/orgs/easystats/people), + contributors, and users alike. +authorcontributions: | + R.T. drafted the paper; all authors contributed to both the writing of the + paper and the conception of the software. +funding: | + This research received no external funding. +conflictsofinterest: | + The authors declare no conflict of interest. +abbreviations: + - short: SOD + long: Statistical outlier detection + - short: SEM + long: Structural equation modelling + - short: SD + long: Standard deviation + - short: MAD + long: Median absolute deviation + - short: IQR + long: Interquartile range + - short: HDI + long: Highest density interval + - short: BCI + long: Bias corrected and accelerated interval + - short: MCD + long: Minimum covariance determinant + - short: ICS + long: invariant coordinate selection + - short: OSF + long: Open Science Framework +output: + rticles::joss_article: + journal: "JOSE" +csl: apa.csl +--- + + + +# Introduction + +Real-life data often contain observations that can be considered *abnormal* when compared to the main population. The cause of it---be it because they belong to a different distribution (originating from a different generative process) or simply being extreme cases, statistically rare but not impossible---can be hard to assess, and the boundaries of "abnormal" difficult to define. + +Nonetheless, the improper handling of these outliers can substantially affect statistical model estimations, biasing effect estimations and weakening the models' predictive performance. +It is thus essential to address this problem in a thoughtful manner. Yet, despite the existence of established recommendations and guidelines, many researchers still do not treat outliers in a consistent manner, or do so using inappropriate strategies [@simmons2011false; @leys2013outliers]. + +One possible reason is that researchers are not aware of the existing recommendations, or do not know how to implement them using their analysis software. In this paper, we show how to follow current best practices for automatic and reproducible statistical outlier detection (SOD) using R and the *{performance}* package [@ludecke2021performance], which is part of the *easystats* ecosystem of packages that build an R framework for easy statistical modeling, visualization, and reporting [@easystatspackage]. + +# Identifying Outliers + +Although many researchers attempt to identify outliers with measures based on the mean (e.g., _z_ scores), those methods are problematic because the mean and standard deviation themselves are not robust to the influence of outliers and they assume normally distributed data (i.e., a Gaussian distribution). Therefore, current guidelines recommend using robust methods to identify outliers, such as those relying on the median as opposed to the mean [@leys2019outliers; @leys2013outliers; @leys2018outliers]. + +Nonetheless, which exact outlier method to use depends on many factors. In some cases, eye-gauging odd observations can be an appropriate solution, though many researchers will favour algorithmic solutions to detect potential outliers, for example, based on a continuous value expressing the observation stands out from the others. + +One of the factors to consider when selecting an algorithmic outlier detection method is the statistical test of interest. When using a regression model, relevant information can be found by identifying observations that do not fit well with the model. This approach, known as model-based outliers detection (as outliers are extracted after the statistical model has been fit), can be contrasted with distribution-based outliers detection, which is based on the distance between an observation and the "center" of its population. Various quantification strategies of this distance exist for the latter, both univariate (involving only one variable at a time) or multivariate (involving multiple variables). + +When no method is readily available to detect model-based outliers, such as for structural equation modelling (SEM), looking for multivariate outliers may be of relevance. For simple tests (_t_ tests or correlations) that compare values of the same variable, it can be appropriate to check for univariate outliers. However, univariate methods can give false positives since _t_ tests and correlations, ultimately, are also models/multivariable statistics. They are in this sense more limited, but we show them nonetheless for educational purposes. + +Importantly, whatever approach researchers choose remains a subjective decision, which usage (and rationale) must be transparently documented and reproducible [@leys2019outliers]. Researchers should commit (ideally in a preregistration) to an outlier treatment method before collecting the data. They should report in the paper their decisions and details of their methods, as well as any deviation from their original plan. These transparency practices can help reduce false positives due to excessive researchers' degrees of freedom (i.e., choice flexibility throughout the analysis). In the following section, we will go through each of the mentioned methods and provide examples on how to implement them with R. + +## Univariate Outliers + +Researchers frequently attempt to identify outliers using measures of deviation from the center of a variable's distribution. One of the most popular such procedure is the _z_ score transformation, which computes the distance in standard deviation (SD) from the mean. However, as mentioned earlier, this popular method is not robust. Therefore, for univariate outliers, it is recommended to use the median along with the Median Absolute Deviation (MAD), which are more robust than the interquartile range or the mean and its standard deviation [@leys2019outliers; @leys2013outliers]. + +Researchers can identify outliers based on robust (i.e., MAD-based) _z_ scores using the `check_outliers()` function of the *{performance}* package, by specifying `method = "zscore_robust"`.^[Note that `check_outliers()` only checks numeric variables.] Although @leys2013outliers suggest a default threshold of 2.5 and @leys2019outliers a threshold of 3, *{performance}* uses by default a less conservative threshold of ~3.29.^[3.29 is an approximation of the two-tailed critical value for _p_ < .001, obtained through `qnorm(p = 1 - 0.001 / 2)`. We chose this threshold for consistency with the thresholds of all our other methods.] That is, data points will be flagged as outliers if they go beyond +/- ~3.29 MAD. Users can adjust this threshold using the `threshold` argument, as demonstrated below. + + +```r +library(performance) + +# Create some artificial outliers and an ID column +data <- rbind(mtcars[1:4], 42, 55) +data <- cbind(car = row.names(data), data) + +outliers <- check_outliers(data, method = "zscore_robust", ID = "car") +outliers +``` + +``` +#> 2 outliers detected: cases 33, 34. +#> - Based on the following method and threshold: zscore_robust (3.291). +#> - For variables: mpg, cyl, disp, hp. +#> +#> ----------------------------------------------------------------------------- +#> +#> The following observations were considered outliers for two or more +#> variables by at least one of the selected methods: +#> +#> Row car n_Zscore_robust +#> 1 33 33 2 +#> 2 34 34 2 +#> +#> ----------------------------------------------------------------------------- +#> Outliers per variable (zscore_robust): +#> +#> $mpg +#> Row car Distance_Zscore_robust +#> 33 33 33 3.709699 +#> 34 34 34 5.848328 +#> +#> $cyl +#> Row car Distance_Zscore_robust +#> 33 33 33 12.14083 +#> 34 34 34 16.52502 +``` + +The row numbers of the detected outliers can be obtained by using `which()` on the output object, which can be used for exclusions for example: + + +```r +which(outliers) +``` + +``` +#> [1] 33 34 +``` + +```r +data_clean <- data[-which(outliers), ] +``` + +All `check_outliers()` output objects possess a `plot()` method, meaning it is also possible to visualize the outliers: + + +```r +library(see) + +plot(outliers) +``` + +\begin{figure} +\includegraphics[width=1\linewidth]{paper_files/figure-latex/univariate_implicit-1} \caption{Visual depiction of outliers using the robust z-score method. The distance represents an aggregate score for variables mpg, cyl, disp, and hp.}\label{fig:univariate_implicit} +\end{figure} + +Other univariate methods are available, such as using the interquartile range (IQR), or based on different intervals, such as the Highest Density Interval (HDI) or the Bias Corrected and Accelerated Interval (BCI). These methods are documented and described in the function's [help page](). + +## Multivariate Outliers + +Univariate outliers can be useful when the focus is on a particular variable, for instance the reaction time, as extreme values might be indicative of inattention or non-task-related behavior^[ Note that they might not be the optimal way of treating reaction time outliers [@ratcliff1993methods; @van1995statistical]]. + +However, in many scenarios, variables of a data set are not independent, and an abnormal observation will impact multiple dimensions. For instance, a participant giving random answers to a questionnaire. In this case, computing the _z_ score for each of the questions might not lead to satisfactory results. Instead, one might want to look at these variables together. + +One common approach for this is to compute multivariate distance metrics such as the Mahalanobis distance. Although the Mahalanobis distance is very popular, just like the regular _z_ scores method, it is not robust and is heavily influenced by the outliers themselves. Therefore, for multivariate outliers, it is recommended to use the Minimum Covariance Determinant, a robust version of the Mahalanobis distance [MCD, @leys2018outliers; @leys2019outliers]. + +In *{performance}*'s `check_outliers()`, one can use this approach with `method = "mcd"`.^[Our default threshold for the MCD method is defined by `stats::qchisq(p = 1 - 0.001, df = ncol(x))`, which again is an approximation of the critical value for _p_ < .001 consistent with the thresholds of our other methods.] + + +```r +outliers <- check_outliers(data, method = "mcd") +outliers +``` + +``` +#> 9 outliers detected: cases 7, 15, 16, 17, 24, 29, 31, 33, 34. +#> - Based on the following method and threshold: mcd (20). +#> - For variables: mpg, cyl, disp, hp. +``` + + +```r +plot(outliers) +``` + +\begin{figure} +\includegraphics[width=1\linewidth]{paper_files/figure-latex/multivariate_implicit-1} \caption{Visual depiction of outliers using the Minimum Covariance Determinant (MCD) method, a robust version of the Mahalanobis distance. The distance represents the MCD scores for variables mpg, cyl, disp, and hp.}\label{fig:multivariate_implicit} +\end{figure} + +Other multivariate methods are available, such as another type of robust Mahalanobis distance that in this case relies on an orthogonalized Gnanadesikan-Kettenring pairwise estimator [@gnanadesikan1972robust]. These methods are documented and described in the function's [help page](https://easystats.github.io/performance/reference/check_outliers.html). + +## Model-Based Outliers + +Working with regression models creates the possibility of using model-based SOD methods. These methods rely on the concept of *leverage*, that is, how much influence a given observation can have on the model estimates. If few observations have a relatively strong leverage/influence on the model, one can suspect that the model's estimates are biased by these observations, in which case flagging them as outliers could prove helpful (see next section, "Handling Outliers"). + +In {performance}, two such model-based SOD methods are currently available: Cook's distance, for regular regression models, and Pareto, for Bayesian models. As such, `check_outliers()` can be applied directly on regression model objects, by simply specifying `method = "cook"` (or `method = "pareto"` for Bayesian models).^[Our default threshold for the Cook method is defined by `stats::qf(0.5, ncol(x), nrow(x) - ncol(x))`, which again is an approximation of the critical value for _p_ < .001 consistent with the thresholds of our other methods.] + + +```r +model <- lm(disp ~ mpg * disp, data = data) +outliers <- check_outliers(model, method = "cook") +outliers +``` + +``` +#> 1 outlier detected: case 34. +#> - Based on the following method and threshold: cook (0.708). +#> - For variable: (Whole model). +``` + +```r +plot(outliers) +``` + +\begin{figure} +\includegraphics[width=1\linewidth]{paper_files/figure-latex/model-1} \caption{Visual depiction of outliers based on Cook's distance (leverage and standardized residuals), based on the fitted model.}\label{fig:model} +\end{figure} + +Table 1 below summarizes which methods to use in which cases, and with what threshold. + + +Table: Summary of Statistical Outlier Detection Methods Recommendations. + +|Statistical Test |Diagnosis Method |Recommended Threshold | +|:------------------------------------------------------------|:------------------------------------------------------|:---------------------------------------------------------| +|Supported regression model |**Model-based**: Cook (or Pareto for Bayesian models) |`qf(0.5, ncol(x), nrow(x) - ncol(x))` (or 0.7 for Pareto) | +|Structural Equation Modeling (or other unsupported model) |**Multivariate**: Minimum Covariance Determinant (MCD) |`qchisq(p = 1 - 0.001, df = ncol(x))` | +|Simple test with few variables (*t* test, correlation, etc.) |**Univariate**: robust *z* scores (MAD) |`qnorm(p = 1 - 0.001 / 2)`, ~ 3.29 | + +## Cook's Distance vs. MCD + +@leys2018outliers report a preference for the MCD method over Cook's distance. This is because Cook's distance removes one observation at a time and checks its corresponding influence on the model each time [@cook1977detection], and flags any observation that has a large influence. In the view of these authors, when there are several outliers, the process of removing a single outlier at a time is problematic as the model remains "contaminated" or influenced by other possible outliers in the model, rendering this method suboptimal in the presence of multiple outliers. + +However, distribution-based approaches are not a silver bullet either, and there are cases where the usage of methods agnostic to theoretical and statistical models of interest might be problematic. For example, a very tall person would be expected to also be much heavier than average, but that would still fit with the expected association between height and weight (i.e., it would be in line with a model such as `weight ~ height`). In contrast, using multivariate outlier detection methods there may flag this person as being an outlier---being unusual on two variables, height and weight---even though the pattern fits perfectly with our predictions. + +In the example below, we plot the raw data and see two possible outliers. The first one falls along the regression line, and is therefore "in line" with our hypothesis. The second one clearly diverges from the regression line, and therefore we can conclude that this outlier may have a disproportionate influence on our model. + + +```r +data <- women[rep(seq_len(nrow(women)), each = 100), ] +data <- rbind(data, c(100, 258), c(100, 200)) +model <- lm(weight ~ height, data) +rempsyc::nice_scatter(data, "height", "weight") +``` + +\begin{figure} +\includegraphics[width=1\linewidth]{paper_files/figure-latex/scatter-1} \caption{Scatter plot of height and weight, with two extreme observations: one model-consistent (top-right) and the other, model-inconsistent (i.e., an outlier; bottom-right).}\label{fig:scatter} +\end{figure} + +Using either the *z*-score or MCD methods, our model-consistent observation will be incorrectly flagged as an outlier or influential observation. + + +```r +outliers <- check_outliers(model, method = c("zscore_robust", "mcd")) +which(outliers) +``` + +``` +#> [1] 1501 1502 +``` + +In contrast, the model-based detection method displays the desired behaviour: it correctly flags the person who is very tall but very light, without flagging the person who is both tall and heavy. + + +```r +outliers <- check_outliers(model, method = "cook") +which(outliers) +``` + +``` +#> [1] 1502 +``` + +```r +plot(outliers) +``` + +\begin{figure} +\includegraphics[width=1\linewidth]{paper_files/figure-latex/model2-1} \caption{The leverage method (Cook's distance) correctly distinguishes the true outlier from the model-consistent extreme observation), based on the fitted model.}\label{fig:model2} +\end{figure} + +Finally, unusual observations happen naturally: extreme observations are expected even when taken from a normal distribution. While statistical models can integrate this "expectation", multivariate outlier methods might be too conservative, flagging too many observations despite belonging to the right generative process. For these reasons, we believe that model-based methods are still preferable to the MCD when using supported regression models. Additionally, if the presence of multiple outliers is a significant concern, regression methods that are more robust to outliers should be considered---like _t_ regression or quantile regression---as they render their precise identification less critical [@mcelreath2020statistical]. + +## Composite Outlier Score + +The *{performance}* package also offers an alternative, consensus-based approach that combines several methods, based on the assumption that different methods provide different angles of looking at a given problem. By applying a variety of methods, one can hope to "triangulate" the true outliers (those consistently flagged by multiple methods) and thus attempt to minimize false positives. + +In practice, this approach computes a composite outlier score, formed of the average of the binary (0 or 1) classification results of each method. It represents the probability that each observation is classified as an outlier by at least one method. The default decision rule classifies rows with composite outlier scores superior or equal to 0.5 as outlier observations (i.e., that were classified as outliers by at least half of the methods). In *{performance}*'s `check_outliers()`, one can use this approach by including all desired methods in the corresponding argument. + + +```r +outliers <- check_outliers(model, method = c("zscore_robust", "mcd", "cook")) +which(outliers) +``` + +``` +#> [1] 1501 1502 +``` + +Outliers (counts or per variables) for individual methods can then be obtained through attributes. For example: + + +```r +attributes(outliers)$outlier_var$zscore_robust +``` + +``` +#> $weight +#> Row Distance_Zscore_robust +#> 1501 1501 6.913530 +#> 1502 1502 3.653492 +#> +#> $height +#> Row Distance_Zscore_robust +#> 1501 1501 5.901794 +#> 1502 1502 5.901794 +``` + +An example sentence for reporting the usage of the composite method could be: + +> Based on a composite outlier score [see the 'check_outliers()' function in the 'performance' R package, @ludecke2021performance] obtained via the joint application of multiple outliers detection algorithms [(a) median absolute deviation (MAD)-based robust _z_ scores, @leys2013outliers; (b) Mahalanobis minimum covariance determinant (MCD), @leys2019outliers; and (c) Cook's distance, @cook1977detection], we excluded two participants that were classified as outliers by at least half of the methods used. + +# Handling Outliers + +The above section demonstrated how to identify outliers using the `check_outliers()` function in the *{performance}* package. But what should we do with these outliers once identified? Although it is common to automatically discard any observation that has been marked as "an outlier" as if it might infect the rest of the data with its statistical ailment, we believe that the use of SOD methods is but one step in the get-to-know-your-data pipeline; a researcher or analyst's _domain knowledge_ must be involved in the decision of how to deal with observations marked as outliers by means of SOD. Indeed, automatic tools can help detect outliers, but they are nowhere near perfect. Although they can be useful to flag suspect data, they can have misses and false alarms, and they cannot replace human eyes and proper vigilance from the researcher. If you do end up manually inspecting your data for outliers, it can be helpful to think of outliers as belonging to different types of outliers, or categories, which can help decide what to do with a given outlier. + +## Error, Interesting, and Random Outliers + +@leys2019outliers distinguish between error outliers, interesting outliers, and random outliers. _Error outliers_ are likely due to human error and should be corrected before data analysis or outright removed since they are invalid observations. _Interesting outliers_ are not due to technical error and may be of theoretical interest; it might thus be relevant to investigate them further even though they should be removed from the current analysis of interest. _Random outliers_ are assumed to be due to chance alone and to belong to the correct distribution and, therefore, should be retained. + +It is recommended to _keep_ observations which are expected to be part of the distribution of interest, even if they are outliers [@leys2019outliers]. However, if it is suspected that the outliers belong to an alternative distribution, then those observations could have a large impact on the results and call into question their robustness, especially if significance is conditional on their inclusion, so should be removed. + +On the other hand, there are also outliers that cannot be detected by statistical tools, but should be found and removed. For example, if we are studying the effects of X on Y among teenagers and we have one observation from a 20-year-old, this observation might not be a _statistical outlier_, but it is an outlier in the _context_ of our research, and should be discarded to allow for valid inferences. + +## Winsorization + +_Removing_ outliers can in this case be a valid strategy, and ideally one would report results with and without outliers to see the extent of their impact on results. This approach however can reduce statistical power. Therefore, some propose a _recoding_ approach, namely, winsorization: bringing outliers back within acceptable limits [e.g., 3 MADs, @tukey1963less]. However, if possible, it is recommended to collect enough data so that even after removing outliers, there is still sufficient statistical power without having to resort to winsorization [@leys2019outliers]. + +The _easystats_ ecosystem makes it easy to incorporate this step into your workflow through the `winsorize()` function of *{datawizard}*, a lightweight R package to facilitate data wrangling and statistical transformations [@patil2022datawizard]. This procedure will bring back univariate outliers within the limits of 'acceptable' values, based either on the percentile, the _z_ score, or its robust alternative based on the MAD. + + +```r +data[1501:1502, ] # See outliers rows +``` + +``` +#> height weight +#> 1501 100 258 +#> 1502 100 200 +``` + +```r +# Winsorizing using the MAD +library(datawizard) +winsorized_data <- winsorize(data, method = "zscore", robust = TRUE, threshold = 3) + +# Values > +/- MAD have been winsorized +winsorized_data[1501:1502, ] +``` + +``` +#> height weight +#> 1501 82.7912 188.3736 +#> 1502 82.7912 188.3736 +``` + +## The Importance of Transparency + +Once again, it is a critical part of a sound outlier treatment that regardless of which SOD method used, it should be reported in a reproducible manner. Ideally, the handling of outliers should be specified *a priori* with as much detail as possible, and preregistered, to limit researchers' degrees of freedom and therefore risks of false positives [@leys2019outliers]. This is especially true given that interesting outliers and random outliers are often times hard to distinguish in practice. Thus, researchers should always prioritize transparency and report all of the following information: (a) how many outliers were identified (including percentage); (b) according to which method and criteria, (c) using which function of which R package (if applicable), and (d) how they were handled (excluded or winsorized, if the latter, using what threshold). If at all possible, (e) the corresponding code script along with the data should be shared on a public repository like the Open Science Framework (OSF), so that the exclusion criteria can be reproduced precisely. + +# Conclusion + +In this paper, we have showed how to investigate outliers using the `check_outliers()` function of the *{performance}* package while following current good practices. However, best practice for outlier treatment does not stop at using appropriate statistical algorithms, but entails respecting existing recommendations, such as preregistration, reproducibility, consistency, transparency, and justification. Ideally, one would additionally also report the package, function, and threshold used (linking to the full code when possible). We hope that this paper and the accompanying `check_outlier()` function of *easystats* will help researchers engage in good research practices while providing a smooth outlier detection experience. + +### Contributions + +R.T. drafted the paper; all authors contributed to both the writing of the paper and the conception of the software. + +### Acknowledgements + +*{performance}* is part of the collaborative [*easystats*](https://github.com/easystats/easystats) ecosystem [@easystatspackage]. Thus, we thank all [members of easystats](https://github.com/orgs/easystats/people), contributors, and users alike. + +### Funding information + +This research received no external funding. + +### Competing Interests + +The authors declare no conflict of interest + +# References diff --git a/papers/JOSE/paper.pdf b/papers/JOSE/paper.pdf new file mode 100644 index 0000000000000000000000000000000000000000..adff65d038baf10000d5bcddcc20fe2cdf1eeab5 GIT binary patch literal 234058 zcmbSyRY03f(C$YmQnW>jOQBeCOV9$vihF?o#fwXDrxYm^cL>lHcbDMq1b5fq7FCp`qKP?xngNZekhzO^qr=vON7Znq0 zb5j>i4ObJFf6wxE#+K%sI#y;b-)OnHxVSjw%&jcHxzO?g0Gv_|whqo3j>e|uoS)3y ztW3>iosB&?C9Pb*s^-p84t9aTCU?iRYcL44GT?tIf{clNE zJA34}f235M&CRS#T^yWgdBnsxWvpyn%$+%9Y>i#a|93%7MRR*gmv30yKpq~Tm>3q= z#o6504$EWVCizX6c1CYo*E0-)gMmKf+(F)BTjU(F~EplCM!zQGPu3%<`q? z1;Y+~EnudlMr>T*9fFVTw&YK!nbiYI&DjNPlPXDGRP$;#EfRL zK4kAD>MSOVe*F0H#SiEUD1%bDtu4x!#K-T_p7Y^_y(;xfORuz0Ul7m^pBPx2-FDEF zqr~IAARro4$buL@E;rI#|F=s^8`$pSWH;f^krNc~@&)3r7O%QNMNuBjM+}rR=&-k~ 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zfVUgWo=gx37AC`H{__Hgiiik_0PTT)*&tZ8fxCc+ziePpY^wjXVLxnOb;5tyz+h|_ z{>ugt``3O#LV{Rv^q+o$5Zw9y+a~cZn}~$OzjBBQO8l!nQLqG7QvK(Cq7b2f$3n!h z-z Less convinced as a scientific research is the major concern. I cannot find a solid contribution for the statistical methodologies, new packages, or sound applications in this study. Almost all the obtained conclusions are known. The readers would be happy to see more convincing results from good real examples from the real world if only the well known statistical methods and packages are used in this study. The tutorial-like results using the examples in R are too weak for an academic paper. It is contributive if the authors can include real examples in different areas to show the power of the used package and present the insight findings, not just show how to use the packages. Then, resubmit the revision as a new paper for review. + +First, we thank the *Mathematics* Editor for their analysis of the paper. We agree that the paper was perhaps less suited to a purely mathematical journal and more so for psychology-oriented journals encouraging open science, good research practices, and good statistical practices. As for the contributions, we believe we make a unique contribution through our proposal of a consensus-based approach to detecting outliers, as well as through our argument that researchers should prefer model-based outlier detection methods over, for example, the Minimum Covariance Determinant (MCD) method which is currently recommended in other guideline documents. We have thus expanded this section to make the contribution more substantial in the revised version of the manuscript, and, as suggested by the Editor, added a real-world example further illustrating our point. + +# Reviewer 1 comments: + +> In this paper, the authors have shown how to search for outliers using the check_outliers() function of the {performance} package while following current good practices. This contribution will help researchers engage in good search practices while providing an outlier detection experience. They cover univariate, multivariate, and model-based statistical outlier detection methods, their recommended threshold, standard output, and plotting methods. The present paper represents the subject of check the outliers, An accessible introduction to identifying statistical outliers in R with easystats. The study design and methods appropriate for the research question. The results presented clearly and accurately. The authors logically explain the findings. I highly recommend the publication of this paper in Mathematics Journal. + +Overall, this reviewer has very positive comments, requests no additional changes, and highly recommend the paper for publication. + +# Reviewer 2 comments: + +> The authors propose the illustration of an R library for detecting outliers. The paper is quite clear, however, the following remarks are provided to improve the article + +> - The word accessible in the title should be removed. + +This has been fixed. + +> - The authors should clarify whether the functions implemented in the library were implemented only for continuous variables or other types of variables are also considered. + +This has been fixed. + +> - The author's reference to the Normal distribution on page 2, line 31 is unclear. They should clarify or delete this sentence. + +This has been fixed. + +> - The reference to the mathematical score is unclear on page 2, line 36. I think this reference should be removed. + +This has been fixed. + +> A critical review on the analysis of outliers is proposed in this article which must be cited + +> Riani, M., & Atkinson, A. C. (2020). Robust regression methods in machine learning. Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery, 10(2), e1359. + +Thank you for this suggestion. We have added a reference to robust regression methods, although we have opted for a different, more suited reference. + +> - Page 3, lines 101-102: It is unclear what the authors mean when referring to BCA, a technique used in non-parametric bootstrapping, but the paper does not mention this. + +At the end of the univariate outliers section, we mention that other methods (in addition to robust *z* scores) are available, and give a few examples, including of the Bias Corrected and Accelerated Interval. Given that we mention that these methods are documented and described in the corresponding functions’ help pages, we think it would not be appropriate to provide an in-depth explanation of these concepts in the current paper since the topic is too tangential to the paper's objectives. + +> - It is necessary to change the x-axis labels of all the figures as the numbers overlap; they should be written in a smaller font or otherwise eliminate some of them since they are not readable. I am talking about the figures referring to the histogram of the outliers. + +This has been fixed. + +> - Page seven, line 146, it is better to write association instead of relationship. + +This has been fixed. + +> - Page 7, line 154, the authors should specify what they mean by compatible regression models. + +This has been fixed. + +> - Page 7, code of the first chunk, the authors use the iqr method, but this is not discussed above. They must add details of all the methods they show in the output. + +This has been fixed. + +> - Page 9, line 247, it is difficult to follow the discussion for those unfamiliar with the R datawizard package. What does it do? How does the proposed function tie in with those in the package? + +This has been fixed. + +> - Page 10, line 272, what does " Registration " mean? + +The word in question was "preregistration", and we think that for a journal such as *Collabra: Psychology*, the readers will be familiar enough with this common concept that there is no need to define it. + +> - Check the reference style because it is not uniform + +We now use APA style. + +# Reviewer 3 comments: + +> The paper outlines techniques for processing data with inhomogeneities, such as outliers. However, the style of the article does not correspond to scientific research. The work is educational and auxiliary in nature and is more in line with educational publications, including popular scientific ones. + +We respectfully disagree with this comment. Good research practices as well as good statistical practices are of paramount importance in this era of the replication crisis, especially in psychology. However, having scattered specialized works covering some of these aspects is not enough for the common, non-expert psychologists. There must also be accessible works that not only gives a cohesive and comprehensive overview of the issues, but also show how to easily apply these guidelines in practice in their own research. We believe we thus make an important applied contribution for psychologists in this regard. + +In addition, we also make a unique theoretical contribution through our proposal of a consensus-based approach to detecting outliers, as well as through our argument that researchers should prefer model-based outlier detection methods over, for example, the Minimum Covariance Determinant (MCD) method which is currently recommended in other guideline documents. 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b/papers/Collabra/cover_letter.Rmd deleted file mode 100644 index 4251c050a..000000000 --- a/papers/Collabra/cover_letter.Rmd +++ /dev/null @@ -1,29 +0,0 @@ ---- -output: pdf_document ---- - -Dear Dr. Vazire, - -We are pleased to submit this paper to *Collabra: Psychology*. - -The paper, titled "Check your outliers! An introduction to identifying statistical outliers in R with *easystats*", provides an overview of current recommendations and best practices regarding the diagnosis and treatment of outliers, a common issue faced by researchers---and a potential source of scientific malpractice. - -It explains the key approaches, highlights recommendations, and shows how users can adopt them in their R analysis with a single function. The manuscript covers univariate, multivariate, and model-based statistical outlier detection methods, their recommended threshold, standard output, and plotting method, among other things. - -Beyond acting like a concise review of outlier treatment procedures and practical tutorial, we also introduce a new outlier-detection method that relies on a consensus-based approach. In this sense, the paper fits well with the "Methodology and Research Practice in Psychology" section of the journal, as it essentially communicates to psychologists how to easily follow some of the best practices in the detection of statistical outlier using currently available open source and free software. This makes the manuscript relevant to data science, behavioural science, and good research and statistical practices more generally. - -As Associated Editor, we would like to suggest Jeffrey Girard, as he is familiar with the *easystats* and R ecosystems, as well as good statistical practices. Additionally, we would like to request a streamlined review, as the manuscript has been rejected within the previous 365 days from the journal *Mathematics*. Accordingly, we provide in this submission a detailed letter that includes prior reviews, the decision letter, as well as how we addressed the reviewers' comments. We have in this regard integrated most of the changes suggested by the reviewers. Note that the previous editors and reviewers have not given their permission for their comments to be openly available at *Collabra: Psychology*. However, although an open review was requested, the reviewers did not sign their reviews. - -Our current submission is original and has been neither published elsewhere nor is currently under consideration for publication elsewhere. All authors have contributed substantially to the software and manuscript. All authors gave final approval to the manuscript and accept to be accountable. We have no conflicts of interest to disclose. We have also read the Transparency and Openness policy of the Editorial Policies of *Collabra: Psychology*. - -Thank you for considering our submission. - -On the behalf of all authors, - -Rémi Thériault - -Department of Psychology, - -Université du Québec à Montréal, - -Montréal, Québec, Canada \ No newline at end of file diff --git a/papers/Collabra/cover_letter.pdf b/papers/Collabra/cover_letter.pdf deleted file mode 100644 index 15650f828a5911b0fdaa1526bfab944c863573a8..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 56483 zcma&M19T=`(=Hs_m`tq6#I|kQ6Wg{Yb~3ST+qNgRZA^@lnauOO&v)McU+eT*UH9(l zs@ip3Ro&U$X(AZ`Axc^*Mku1mnZ5-mT09y&D_v744h}qOc|2-iD+Mb&Y5_cTx_7-C z9<`8(y(S(P7nFge{%)0Cz80cB) z8$i7~+u7S1=vY8GFZrvA$F4NOwx3rVq-K{V%YHfHC1tK?TRc&6IdzcS;!gz@-l}a> z633Rk%Dp}YM##iDO+WPGL<02%fpEX?jBpIptbKY2JlHyqgy(+VwGyo+@1a9`INLNK z?vv`5{Y+$gCv*Oa+B$8zuud$B)QZXHF5>5P7Rn&=M(@|Y{Pwgtzv_WvC|lJMX`u4e 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zgeBE~@GE2YpRx{0vKbcXp1bTC>ra)a5wLS!m22v1rW?~Pw1jwKwFeEWj`dU?o9hcq zY1xsJF=+m7YO+L4LHS-mSiz)??X>mn8-5ZhqEY+zt~A~9i^2suG#b#bLg89YmHLI_ zGOaRy_(3ZbQl9NxsUVoyQy#+#q~}ol=Hc86jvXWdc7-ZnUhDxp!K;Qj*Zyv7XRF7-81k4N$G> zx&eC(_t+P)p;Tg5Sp4>Gn{rWCCBfA4MhA@o$tR?;2?b|_jfNiG-qt^JfM}8An*MM$ zRKw%rJ>+LCpA9gr6E8B#PA525UQU{*QSw)?oM;n-cClBkeJDo5E&78SGb$8=EA0Nz5QD;N#qWcyN-t&{5vjGRmfB2_Ag3FRB}jeJu|S8^U74u*knnI; z>f4oxm%C!X#tBACk}+)12;o~dW!n94_6#Qj9o%=t^OjE~ageQa(UTNYvs3gWZs=i! ziiKY#+rlp*pu(y9Z2bpHg;U{03qO+G4)rpl9qQtH{3?em{6hS9sB5Q6Bq0kVlDZNk zlG2JfA~T@7PRozfspZFC@=MYac)8OD<#MNIAj(%>UEI!ZyMLu3k3Er!(3hVj$7y}5 z@;!KV&Mdk_LLd8em-6ih&KkptqN5yRkKGaUF6StjLLmgVq&l#inGh1S5W1+R z5R$942Y~Yf&D@>J^#Fi?Rl^T*OaL8=4iSGz3i|&?Qr@HsMD+vC1-}Misj)f9>5=T= zH!AtfAFHp1)Vz9Z^_A%>l9>s9FH*+lRIzua=Ww=fzG-An!|sBI`7nI*txt9M#KM7u znG{d)LEi&iZ}VrP1JyrHRm>#jIX=>0Uu~RSBP=?p@BP-d@E=VV=Qa)li=8L_Vg;jlSq&+t%D0dk@_EMe34qjx94zVg@HbTOF0uY2@VnYP>-H zAguXYH7&8OXIEO`>b^DP!OF~2rmc3_UyJ%{Mjm@NTxZ=sl-4rrr}yc}%;dYKZ_`MP zz3@+aQne0kvS<;xyGu6r{HENQ1mUXrw+tYwQ1hjbAr&~5p|JLVW!-U2Hc-b+(4)U^P*t_?X-aHcX;edx|WDwvP zE0iUqTsHBjdzscnMo<>~)Hu2wgi_ zX5lJBDeHGJOw)Jlp7MHPF8?E$(8&CE#pTMx!z(O@wz|ZhWv<0%T!*f#+Y>!AbclD8 zXlvxPC-j-EPl7$a=G~e;crr7sZc1*pJZ&yAV8hb_`q~#)9cB4DbkLQ%(>h#zVt#L} zv>tq5FLLkU1!Oj5ExD;)lHFSRK1Uv&bq4v-NtxX3uv-J;(9Jio4gP#pu>&93xo%(O zXC?4kOefcQ-N*FmZWt_6N=?dSCujS z8R!bNIx8ogybN@*O$+ryj(w7<Xp1kaC^wgmdY5zkbmkHqA z+-~%^^@#M&yBv1gU5-d+2FGBc!s!F(W=Vob@ZLeh6I*T6%cY($W+7(SUuB+!2?~9mQSmq8=_xUfUj+)zCn7I=>2NVGsDi^yUu< zGRb{wKM+{BIg?`K$#SE*bJuG`r?_j9SyWI&E~N2qqZbr+@r&aaGiVN;WZ>7Lw4bVP zMmY%49UQ@nDiVf4z)%=aPiuOzoM{XtWw;rYOyKD3=D~ZAt0s26e%w$lYJNzMESiW0XMR~677J4MQy&TiuJ+||C>-&pIir!_JK*v-1R9I^aa;uO4EphS zXgreeiemK_Y)V9u|ut{Fqa4BJe-QVYr3P@^P`)rN?72 z?15zx16Wx>a8v3D3itfN571~VX#SoBH=&-pBMp3sn!lsrdODExZiJ2|9*fh$Xc37d xZG). - -## Multivariate Outliers - -Univariate outliers can be useful when the focus is on a particular variable, for instance the reaction time, as extreme values might be indicative of inattention or non-task-related behavior^[ Note that they might not be the optimal way of treating reaction time outliers [@ratcliff1993methods; @van1995statistical]]. - -However, in many scenarios, variables of a data set are not independent, and an abnormal observation will impact multiple dimensions. For instance, a participant giving random answers to a questionnaire. In this case, computing the _z_ score for each of the questions might not lead to satisfactory results. Instead, one might want to look at these variables together. - -One common approach for this is to compute multivariate distance metrics such as the Mahalanobis distance. Although the Mahalanobis distance is very popular, just like the regular _z_ scores method, it is not robust and is heavily influenced by the outliers themselves. Therefore, for multivariate outliers, it is recommended to use the Minimum Covariance Determinant, a robust version of the Mahalanobis distance [MCD, @leys2018outliers; @leys2019outliers]. - -In *{performance}*'s `check_outliers()`, one can use this approach with `method = "mcd"`.^[Our default threshold for the MCD method is defined by `stats::qchisq(p = 1 - 0.001, df = ncol(x))`, which again is an approximation of the critical value for _p_ < .001 consistent with the thresholds of our other methods.] - -```{r multivariate} -outliers <- check_outliers(data, method = "mcd") -outliers -``` - -```{r multivariate_plot, eval=FALSE} -plot(outliers) -``` - -```{r multivariate_implicit, fig.cap = "Visual depiction of outliers using the Minimum Covariance Determinant (MCD) method, a robust version of the Mahalanobis distance. The distance represents the MCD scores for variables mpg, cyl, disp, and hp.", echo=FALSE} -plot(outliers) + - ggplot2::theme(axis.text.x = ggplot2::element_text( - angle = 45, size = 7 -)) -``` - -Other multivariate methods are available, such as another type of robust Mahalanobis distance that in this case relies on an orthogonalized Gnanadesikan-Kettenring pairwise estimator [@gnanadesikan1972robust]. These methods are documented and described in the function's [help page](https://easystats.github.io/performance/reference/check_outliers.html). - -## Model-Based Outliers - -Working with regression models creates the possibility of using model-based SOD methods. These methods rely on the concept of *leverage*, that is, how much influence a given observation can have on the model estimates. If few observations have a relatively strong leverage/influence on the model, one can suspect that the model's estimates are biased by these observations, in which case flagging them as outliers could prove helpful (see next section, "Handling Outliers"). - -In {performance}, two such model-based SOD methods are currently available: Cook's distance, for regular regression models, and Pareto, for Bayesian models. As such, `check_outliers()` can be applied directly on regression model objects, by simply specifying `method = "cook"` (or `method = "pareto"` for Bayesian models).^[Our default threshold for the Cook method is defined by `stats::qf(0.5, ncol(x), nrow(x) - ncol(x))`, which again is an approximation of the critical value for _p_ < .001 consistent with the thresholds of our other methods.] - -```{r model, fig.cap = "Visual depiction of outliers based on Cook's distance (leverage and standardized residuals), based on the fitted model."} -model <- lm(disp ~ mpg * disp, data = data) -outliers <- check_outliers(model, method = "cook") -outliers - -plot(outliers) -``` - -Table 1 below summarizes which methods to use in which cases, and with what threshold. - -```{r, echo=FALSE} -df <- data.frame( - `Statistical Test` = c( - "Supported regression model", - "Structural Equation Modeling (or other unsupported model)", - "Simple test with few variables (*t* test, correlation, etc.)"), - `Diagnosis Method` = c( - "**Model-based**: Cook (or Pareto for Bayesian models)", - "**Multivariate**: Minimum Covariance Determinant (MCD)", - "**Univariate**: robust *z* scores (MAD)"), - `Recommended Threshold` = c( - "`qf(0.5, ncol(x), nrow(x) - ncol(x))` (or 0.7 for Pareto)", - "`qchisq(p = 1 - 0.001, df = ncol(x))`", - "`qnorm(p = 1 - 0.001 / 2)`, ~ 3.29") -) -knitr::kable( - df, col.names = gsub("[.]", " ", names(df)), - caption = "Summary of Statistical Outlier Detection Methods Recommendations.", longtable = TRUE) -``` - -## Cook's Distance vs. MCD - -@leys2018outliers report a preference for the MCD method over Cook's distance. This is because Cook's distance removes one observation at a time and checks its corresponding influence on the model each time [@cook1977detection], and flags any observation that has a large influence. In the view of these authors, when there are several outliers, the process of removing a single outlier at a time is problematic as the model remains "contaminated" or influenced by other possible outliers in the model, rendering this method suboptimal in the presence of multiple outliers. - -However, distribution-based approaches are not a silver bullet either, and there are cases where the usage of methods agnostic to theoretical and statistical models of interest might be problematic. For example, a very tall person would be expected to also be much heavier than average, but that would still fit with the expected association between height and weight (i.e., it would be in line with a model such as `weight ~ height`). In contrast, using multivariate outlier detection methods there may flag this person as being an outlier---being unusual on two variables, height and weight---even though the pattern fits perfectly with our predictions. - -In the example below, we plot the raw data and see two possible outliers. The first one falls along the regression line, and is therefore "in line" with our hypothesis. The second one clearly diverges from the regression line, and therefore we can conclude that this outlier may have a disproportionate influence on our model. - -```{r scatter, fig.cap = "Scatter plot of height and weight, with two extreme observations: one model-consistent (top-right) and the other, model-inconsistent (i.e., an outlier; bottom-right)."} -data <- women[rep(seq_len(nrow(women)), each = 100), ] -data <- rbind(data, c(100, 258), c(100, 200)) -model <- lm(weight ~ height, data) -rempsyc::nice_scatter(data, "height", "weight") -``` - -Using either the *z*-score or MCD methods, our model-consistent observation will be incorrectly flagged as an outlier or influential observation. - -```{r} -outliers <- check_outliers(model, method = c("zscore_robust", "mcd")) -which(outliers) -``` - -In contrast, the model-based detection method displays the desired behaviour: it correctly flags the person who is very tall but very light, without flagging the person who is both tall and heavy. - -```{r model2, fig.cap = "The leverage method (Cook's distance) correctly distinguishes the true outlier from the model-consistent extreme observation), based on the fitted model."} -outliers <- check_outliers(model, method = "cook") -which(outliers) -plot(outliers) -``` - -Finally, unusual observations happen naturally: extreme observations are expected even when taken from a normal distribution. While statistical models can integrate this "expectation", multivariate outlier methods might be too conservative, flagging too many observations despite belonging to the right generative process. For these reasons, we believe that model-based methods are still preferable to the MCD when using supported regression models. Additionally, if the presence of multiple outliers is a significant concern, regression methods that are more robust to outliers should be considered---like _t_ regression or quantile regression---as they render their precise identification less critical [@mcelreath2020statistical]. - -## Composite Outlier Score - -The *{performance}* package also offers an alternative, consensus-based approach that combines several methods, based on the assumption that different methods provide different angles of looking at a given problem. By applying a variety of methods, one can hope to "triangulate" the true outliers (those consistently flagged by multiple methods) and thus attempt to minimize false positives. - -In practice, this approach computes a composite outlier score, formed of the average of the binary (0 or 1) classification results of each method. It represents the probability that each observation is classified as an outlier by at least one method. The default decision rule classifies rows with composite outlier scores superior or equal to 0.5 as outlier observations (i.e., that were classified as outliers by at least half of the methods). In *{performance}*'s `check_outliers()`, one can use this approach by including all desired methods in the corresponding argument. - -```{r multimethod, fig.cap = "Visual depiction of outliers using several different statistical outlier detection methods."} -outliers <- check_outliers(model, method = c("zscore_robust", "mcd", "cook")) -which(outliers) -``` - -Outliers (counts or per variables) for individual methods can then be obtained through attributes. For example: - -```{r} -attributes(outliers)$outlier_var$zscore_robust -``` - -An example sentence for reporting the usage of the composite method could be: - -> Based on a composite outlier score [see the 'check_outliers()' function in the 'performance' R package, @ludecke2021performance] obtained via the joint application of multiple outliers detection algorithms [(a) median absolute deviation (MAD)-based robust _z_ scores, @leys2013outliers; (b) Mahalanobis minimum covariance determinant (MCD), @leys2019outliers; and (c) Cook's distance, @cook1977detection], we excluded two participants that were classified as outliers by at least half of the methods used. - -# Handling Outliers - -The above section demonstrated how to identify outliers using the `check_outliers()` function in the *{performance}* package. But what should we do with these outliers once identified? Although it is common to automatically discard any observation that has been marked as "an outlier" as if it might infect the rest of the data with its statistical ailment, we believe that the use of SOD methods is but one step in the get-to-know-your-data pipeline; a researcher or analyst's _domain knowledge_ must be involved in the decision of how to deal with observations marked as outliers by means of SOD. Indeed, automatic tools can help detect outliers, but they are nowhere near perfect. Although they can be useful to flag suspect data, they can have misses and false alarms, and they cannot replace human eyes and proper vigilance from the researcher. If you do end up manually inspecting your data for outliers, it can be helpful to think of outliers as belonging to different types of outliers, or categories, which can help decide what to do with a given outlier. - -## Error, Interesting, and Random Outliers - -@leys2019outliers distinguish between error outliers, interesting outliers, and random outliers. _Error outliers_ are likely due to human error and should be corrected before data analysis or outright removed since they are invalid observations. _Interesting outliers_ are not due to technical error and may be of theoretical interest; it might thus be relevant to investigate them further even though they should be removed from the current analysis of interest. _Random outliers_ are assumed to be due to chance alone and to belong to the correct distribution and, therefore, should be retained. - -It is recommended to _keep_ observations which are expected to be part of the distribution of interest, even if they are outliers [@leys2019outliers]. However, if it is suspected that the outliers belong to an alternative distribution, then those observations could have a large impact on the results and call into question their robustness, especially if significance is conditional on their inclusion, so should be removed. - -On the other hand, there are also outliers that cannot be detected by statistical tools, but should be found and removed. For example, if we are studying the effects of X on Y among teenagers and we have one observation from a 20-year-old, this observation might not be a _statistical outlier_, but it is an outlier in the _context_ of our research, and should be discarded to allow for valid inferences. - -## Winsorization - -_Removing_ outliers can in this case be a valid strategy, and ideally one would report results with and without outliers to see the extent of their impact on results. This approach however can reduce statistical power. Therefore, some propose a _recoding_ approach, namely, winsorization: bringing outliers back within acceptable limits [e.g., 3 MADs, @tukey1963less]. However, if possible, it is recommended to collect enough data so that even after removing outliers, there is still sufficient statistical power without having to resort to winsorization [@leys2019outliers]. - -The _easystats_ ecosystem makes it easy to incorporate this step into your workflow through the `winsorize()` function of *{datawizard}*, a lightweight R package to facilitate data wrangling and statistical transformations [@patil2022datawizard]. This procedure will bring back univariate outliers within the limits of 'acceptable' values, based either on the percentile, the _z_ score, or its robust alternative based on the MAD. - -```{r winsorization} -data[1501:1502, ] # See outliers rows - -# Winsorizing using the MAD -library(datawizard) -winsorized_data <- winsorize(data, method = "zscore", robust = TRUE, threshold = 3) - -# Values > +/- MAD have been winsorized -winsorized_data[1501:1502, ] -``` - -## The Importance of Transparency - -Once again, it is a critical part of a sound outlier treatment that regardless of which SOD method used, it should be reported in a reproducible manner. Ideally, the handling of outliers should be specified *a priori* with as much detail as possible, and preregistered, to limit researchers' degrees of freedom and therefore risks of false positives [@leys2019outliers]. This is especially true given that interesting outliers and random outliers are often times hard to distinguish in practice. Thus, researchers should always prioritize transparency and report all of the following information: (a) how many outliers were identified (including percentage); (b) according to which method and criteria, (c) using which function of which R package (if applicable), and (d) how they were handled (excluded or winsorized, if the latter, using what threshold). If at all possible, (e) the corresponding code script along with the data should be shared on a public repository like the Open Science Framework (OSF), so that the exclusion criteria can be reproduced precisely. - -# Conclusion - -In this paper, we have showed how to investigate outliers using the `check_outliers()` function of the *{performance}* package while following current good practices. However, best practice for outlier treatment does not stop at using appropriate statistical algorithms, but entails respecting existing recommendations, such as preregistration, reproducibility, consistency, transparency, and justification. Ideally, one would additionally also report the package, function, and threshold used (linking to the full code when possible). We hope that this paper and the accompanying `check_outlier()` function of *easystats* will help researchers engage in good research practices while providing a smooth outlier detection experience. - -### Contributions - -Author 1 drafted the paper; all authors contributed to both the writing of the paper and the conception of the software. - -### Acknowledgements - -*{performance}* is part of the collaborative [*easystats*](https://github.com/easystats/easystats) ecosystem [@easystatspackage]. 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I cannot find a solid contribution for the statistical methodologies, new packages, or sound applications in this study. Almost all the obtained conclusions are known. The readers would be happy to see more convincing results from good real examples from the real world if only the well known statistical methods and packages are used in this study. The tutorial-like results using the examples in R are too weak for an academic paper. It is contributive if the authors can include real examples in different areas to show the power of the used package and present the insight findings, not just show how to use the packages. Then, resubmit the revision as a new paper for review. - -First, we thank the *Mathematics* Editor for their analysis of the paper. We agree that the paper was perhaps less suited to a purely mathematical journal and more so for psychology-oriented journals encouraging open science, good research practices, and good statistical practices. As for the contributions, we believe we make a unique contribution through our proposal of a consensus-based approach to detecting outliers, as well as through our argument that researchers should prefer model-based outlier detection methods over, for example, the Minimum Covariance Determinant (MCD) method which is currently recommended in other guideline documents. We have thus expanded this section to make the contribution more substantial in the revised version of the manuscript, and, as suggested by the Editor, added a real-world example further illustrating our point. - -# Reviewer 1 comments: - -> In this paper, the authors have shown how to search for outliers using the check_outliers() function of the {performance} package while following current good practices. This contribution will help researchers engage in good search practices while providing an outlier detection experience. They cover univariate, multivariate, and model-based statistical outlier detection methods, their recommended threshold, standard output, and plotting methods. The present paper represents the subject of check the outliers, An accessible introduction to identifying statistical outliers in R with easystats. The study design and methods appropriate for the research question. The results presented clearly and accurately. The authors logically explain the findings. I highly recommend the publication of this paper in Mathematics Journal. - -Overall, this reviewer has very positive comments, requests no additional changes, and highly recommend the paper for publication. - -# Reviewer 2 comments: - -> The authors propose the illustration of an R library for detecting outliers. The paper is quite clear, however, the following remarks are provided to improve the article - -> - The word accessible in the title should be removed. - -This has been fixed. - -> - The authors should clarify whether the functions implemented in the library were implemented only for continuous variables or other types of variables are also considered. - -This has been fixed. - -> - The author's reference to the Normal distribution on page 2, line 31 is unclear. They should clarify or delete this sentence. - -This has been fixed. - -> - The reference to the mathematical score is unclear on page 2, line 36. I think this reference should be removed. - -This has been fixed. - -> A critical review on the analysis of outliers is proposed in this article which must be cited - -> Riani, M., & Atkinson, A. C. (2020). Robust regression methods in machine learning. Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery, 10(2), e1359. - -Thank you for this suggestion. We have added a reference to robust regression methods, although we have opted for a different, more suited reference. - -> - Page 3, lines 101-102: It is unclear what the authors mean when referring to BCA, a technique used in non-parametric bootstrapping, but the paper does not mention this. - -At the end of the univariate outliers section, we mention that other methods (in addition to robust *z* scores) are available, and give a few examples, including of the Bias Corrected and Accelerated Interval. Given that we mention that these methods are documented and described in the corresponding functions’ help pages, we think it would not be appropriate to provide an in-depth explanation of these concepts in the current paper since the topic is too tangential to the paper's objectives. - -> - It is necessary to change the x-axis labels of all the figures as the numbers overlap; they should be written in a smaller font or otherwise eliminate some of them since they are not readable. I am talking about the figures referring to the histogram of the outliers. - -This has been fixed. - -> - Page seven, line 146, it is better to write association instead of relationship. - -This has been fixed. - -> - Page 7, line 154, the authors should specify what they mean by compatible regression models. - -This has been fixed. - -> - Page 7, code of the first chunk, the authors use the iqr method, but this is not discussed above. They must add details of all the methods they show in the output. - -This has been fixed. - -> - Page 9, line 247, it is difficult to follow the discussion for those unfamiliar with the R datawizard package. What does it do? How does the proposed function tie in with those in the package? - -This has been fixed. - -> - Page 10, line 272, what does " Registration " mean? - -The word in question was "preregistration", and we think that for a journal such as *Collabra: Psychology*, the readers will be familiar enough with this common concept that there is no need to define it. - -> - Check the reference style because it is not uniform - -We now use APA style. - -# Reviewer 3 comments: - -> The paper outlines techniques for processing data with inhomogeneities, such as outliers. However, the style of the article does not correspond to scientific research. The work is educational and auxiliary in nature and is more in line with educational publications, including popular scientific ones. - -We respectfully disagree with this comment. Good research practices as well as good statistical practices are of paramount importance in this era of the replication crisis, especially in psychology. However, having scattered specialized works covering some of these aspects is not enough for the common, non-expert psychologists. There must also be accessible works that not only gives a cohesive and comprehensive overview of the issues, but also show how to easily apply these guidelines in practice in their own research. We believe we thus make an important applied contribution for psychologists in this regard. - -In addition, we also make a unique theoretical contribution through our proposal of a consensus-based approach to detecting outliers, as well as through our argument that researchers should prefer model-based outlier detection methods over, for example, the Minimum Covariance Determinant (MCD) method which is currently recommended in other guideline documents. 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An introduction to identifying statistical outliers in R with *easystats*" has been submitted to the Journal *Mathematics* before, and has been rejected. - -# Editor comments: - -> Less convinced as a scientific research is the major concern. I cannot find a solid contribution for the statistical methodologies, new packages, or sound applications in this study. Almost all the obtained conclusions are known. The readers would be happy to see more convincing results from good real examples from the real world if only the well known statistical methods and packages are used in this study. The tutorial-like results using the examples in R are too weak for an academic paper. It is contributive if the authors can include real examples in different areas to show the power of the used package and present the insight findings, not just show how to use the packages. Then, resubmit the revision as a new paper for review. - -First, we thank the *Mathematics* Editor for their analysis of the paper. We agree that the paper was perhaps less suited to a purely mathematical journal and more so for psychology-oriented journals encouraging open science, good research practices, and good statistical practices. As for the contributions, we believe we make a unique contribution through our proposal of a consensus-based approach to detecting outliers, as well as through our argument that researchers should prefer model-based outlier detection methods over, for example, the Minimum Covariance Determinant (MCD) method which is currently recommended in other guideline documents. We have thus expanded this section to make the contribution more substantial in the revised version of the manuscript, and, as suggested by the Editor, added a real-world example further illustrating our point. - -# Reviewer 1 comments: - -> In this paper, the authors have shown how to search for outliers using the check_outliers() function of the {performance} package while following current good practices. This contribution will help researchers engage in good search practices while providing an outlier detection experience. They cover univariate, multivariate, and model-based statistical outlier detection methods, their recommended threshold, standard output, and plotting methods. The present paper represents the subject of check the outliers, An accessible introduction to identifying statistical outliers in R with easystats. The study design and methods appropriate for the research question. The results presented clearly and accurately. The authors logically explain the findings. I highly recommend the publication of this paper in Mathematics Journal. - -Overall, this reviewer has very positive comments, requests no additional changes, and highly recommend the paper for publication. - -# Reviewer 2 comments: - -> The authors propose the illustration of an R library for detecting outliers. The paper is quite clear, however, the following remarks are provided to improve the article - -> - The word accessible in the title should be removed. - -This has been fixed. - -> - The authors should clarify whether the functions implemented in the library were implemented only for continuous variables or other types of variables are also considered. - -This has been fixed. - -> - The author's reference to the Normal distribution on page 2, line 31 is unclear. They should clarify or delete this sentence. - -This has been fixed. - -> - The reference to the mathematical score is unclear on page 2, line 36. I think this reference should be removed. - -This has been fixed. - -> A critical review on the analysis of outliers is proposed in this article which must be cited - -> Riani, M., & Atkinson, A. C. (2020). Robust regression methods in machine learning. Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery, 10(2), e1359. - -Thank you for this suggestion. We have added a reference to robust regression methods, although we have opted for a different, more suited reference. - -> - Page 3, lines 101-102: It is unclear what the authors mean when referring to BCA, a technique used in non-parametric bootstrapping, but the paper does not mention this. - -At the end of the univariate outliers section, we mention that other methods (in addition to robust *z* scores) are available, and give a few examples, including of the Bias Corrected and Accelerated Interval. Given that we mention that these methods are documented and described in the corresponding functions’ help pages, we think it would not be appropriate to provide an in-depth explanation of these concepts in the current paper since the topic is too tangential to the paper's objectives. - -> - It is necessary to change the x-axis labels of all the figures as the numbers overlap; they should be written in a smaller font or otherwise eliminate some of them since they are not readable. I am talking about the figures referring to the histogram of the outliers. - -This has been fixed. - -> - Page seven, line 146, it is better to write association instead of relationship. - -This has been fixed. - -> - Page 7, line 154, the authors should specify what they mean by compatible regression models. - -This has been fixed. - -> - Page 7, code of the first chunk, the authors use the iqr method, but this is not discussed above. They must add details of all the methods they show in the output. - -This has been fixed. - -> - Page 9, line 247, it is difficult to follow the discussion for those unfamiliar with the R datawizard package. What does it do? How does the proposed function tie in with those in the package? - -This has been fixed. - -> - Page 10, line 272, what does " Registration " mean? - -The word in question was "preregistration", and we think that for a journal such as *Collabra: Psychology*, the readers will be familiar enough with this common concept that there is no need to define it. - -> - Check the reference style because it is not uniform - -We now use APA style. - -# Reviewer 3 comments: - -> The paper outlines techniques for processing data with inhomogeneities, such as outliers. However, the style of the article does not correspond to scientific research. The work is educational and auxiliary in nature and is more in line with educational publications, including popular scientific ones. - -We respectfully disagree with this comment. Good research practices as well as good statistical practices are of paramount importance in this era of the replication crisis, especially in psychology. However, having scattered specialized works covering some of these aspects is not enough for the common, non-expert psychologists. There must also be accessible works that not only gives a cohesive and comprehensive overview of the issues, but also show how to easily apply these guidelines in practice in their own research. We believe we thus make an important applied contribution for psychologists in this regard. - -In addition, we also make a unique theoretical contribution through our proposal of a consensus-based approach to detecting outliers, as well as through our argument that researchers should prefer model-based outlier detection methods over, for example, the Minimum Covariance Determinant (MCD) method which is currently recommended in other guideline documents. 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zFXJSW=(U0uFhrco;ffPw_9iC8Mg5;Xx67sX2{avCW-v51ZgC5YC4Tqhy2?gfMI{*hcPwY+%@qI%wrr2FcF=-YHs`GT;o9 z7KC6n7|TX(7yV}_tsHztpZfntrzo#gItQ@TMqzvof9?hCr~?)$ZRYcAgoN9aIdBpZ zKp$N0mx*f5mVT*Z*gj_t?4vC4;d>aOz%U}rT7@5uz^2u~QEF^O=CQjzE z_#7I8#o;h$G&wtce3bVNIoC5DydXiC*nchyWpHsWPDVKbgiPlGF>!E=MHa$5A&bYN zGcgQToU63A?_4`7q25aB-fK&8C@>~q$JBm9mQVF-|NqzEE5ZL?H-K~hx#Vv#_aAos z!>+%@fxor*AMN^wU4M%Me{1nS+Vx*!7wKy%0CFUIlOz!6>wGPYDiS9mcLTpShEVX; z|54=s3K)|` } - { s nameptr "{vv~}{ll}{, jj}{, f{.}}." format.name$ 't := - nameptr #1 > - { - nameptr #10 - #1 + = - numnames #10 - > and - { "others" 't := - #1 'namesleft := } - 'skip$ - if$ - namesleft #1 > - { "; " * t * } - { - s nameptr "{ll}" format.name$ duplicate$ "others" = - { 't := } - { pop$ } - if$ - numnames #2 > - { "" * } - 'skip$ - if$ - t "others" = - {"; " * " et~al." * } - { "; " * t * } - if$ - } - if$ - } - 't - if$ - nameptr #1 + 'nameptr := - namesleft #1 - 'namesleft := - } - while$ -} - -FUNCTION {format.key} -{ empty$ - { key field.or.null } - { "" } - if$ -} - -FUNCTION {format.authors} -{ author empty$ - { "" } - { author format.names } - if$ -} - -FUNCTION {format.editors} -{ editor empty$ - { "" } - { editor format.names - editor num.names$ #1 > - { ", Eds." * } - { ", Ed." * } - if$ - } - if$ -} - - - - -FUNCTION {format.title} -{ title empty$ - { "" } - { title} - if$ -} - -FUNCTION {format.number.patent} -{ number empty$ - { "" } - { nationality empty$ - { number} - { nationality " " * number *} - if$ - } - if$ -} - -FUNCTION {format.full.names} -{'s := - #1 'nameptr := - s num.names$ 'numnames := - numnames 'namesleft := - { namesleft #0 > } - { s nameptr - "{vv~}{ll}" format.name$ 't := - nameptr #1 > - { - namesleft #1 > - { ", " * t * } - { - numnames #2 > - { "," * } - 'skip$ - if$ - t "others" = - { " et~al." * } - { " and " * t * } - if$ - } - if$ - } - 't - if$ - nameptr #1 + 'nameptr := - namesleft #1 - 'namesleft := - } - while$ -} - -FUNCTION {author.editor.full} -{ author empty$ - { editor empty$ - { "" } - { editor format.full.names } - if$ - } - { author format.full.names } - if$ -} - - - -FUNCTION {author.full} -{ author empty$ - { "" } - { author format.full.names } - if$ -} - -FUNCTION {editor.full} -{ editor empty$ - { "" } - { editor format.full.names } - if$ -} - -FUNCTION {make.full.names} -{ type$ "book" = - type$ "inbook" = - or - 'author.editor.full - { type$ "proceedings" = - 'editor.full - 'author.full - if$ - } - if$ -} - -FUNCTION {output.bibitem} -{ newline$ - "\bibitem[" write$ - label write$ - ")" make.full.names duplicate$ short.list = - { pop$ } - { * } - if$ - "]{" * write$ - cite$ write$ - "}" write$ - newline$ - "" - before.all 'output.state := -} - -FUNCTION {n.dashify} -{ 't := - "" - { t empty$ not } - { t #1 #1 substring$ "-" = - { t #1 #2 substring$ "--" = not - { "--" * - t #2 global.max$ substring$ 't := - } - { { t #1 #1 substring$ "-" = } - { "-" * - t #2 global.max$ substring$ 't := - } - while$ - } - if$ - } - { t #1 #1 substring$ * - t #2 global.max$ substring$ 't := - } - if$ - } - while$ -} - - -FUNCTION {format.date} -{ year empty$ - { month empty$ - { "" } - { "there's a month but no year in " cite$ * warning$ - month - } - if$ - } - { " " year embolden * } - if$ -} - -FUNCTION {format.bdate} -{ year empty$ - { month empty$ - { "" } - { "there's a month but no year in " cite$ * warning$ - month - } - if$ - } - { " " year * } - if$ -} - -FUNCTION {format.pdate} -{ year empty$ - { month empty$ - { "" } - { "there's a month but no year in " cite$ * warning$ - month - } - if$ - } - { month empty$ - { " " year * } - { " " month * ", " * year * } - if$} - if$ -} - -FUNCTION {format.btitle} -{ title emphasize -} - -FUNCTION {tie.or.space.connect} -{ duplicate$ text.length$ #3 < - { "~" } - { " " } - if$ - swap$ * * -} - -FUNCTION {either.or.check} -{ empty$ - 'pop$ - { "can't use both " swap$ * " fields in " * cite$ * warning$ } - if$ -} - -FUNCTION {format.bvolume} -{ volume empty$ - { "" } - { "Vol." volume tie.or.space.connect - series empty$ - 'skip$ - { ", " * series emphasize * } - if$ - "volume and number" number either.or.check - } - if$ -} - -FUNCTION {format.number.series} -{ volume empty$ - { number empty$ - { series field.or.null } - { output.state mid.sentence = - { "number" } - { "Number" } - if$ - number tie.or.space.connect - series empty$ - { "there's a number but no series in " cite$ * warning$ } - { " in " * series * } - if$ - } - if$ - } - { "" } - if$ -} - -FUNCTION {format.edition} -{ edition empty$ - { "" } - { output.state mid.sentence = - { edition "l" change.case$ " ed." * } - { edition "t" change.case$ " ed." * } - if$ - } - if$ -} - -INTEGERS { multiresult } - -FUNCTION {multi.page.check} -{ 't := - #0 'multiresult := - { multiresult not - t empty$ not - and - } - { t #1 #1 substring$ - duplicate$ "-" = - swap$ duplicate$ "," = - swap$ "+" = - or or - { #1 'multiresult := } - { t #2 global.max$ substring$ 't := } - if$ - } - while$ - multiresult -} - -FUNCTION {format.pages} -{ pages empty$ - { "" } - { pages multi.page.check - { "pp." pages n.dashify tie.or.space.connect } - { "p." pages tie.or.space.connect } - if$ - } - if$ -} - -FUNCTION {format.vol.num.pages} -{ volume emphasize field.or.null - number empty$ - 'skip$ - { - volume empty$ - { "there's a number but no volume in " cite$ * warning$ } - 'skip$ - if$ - } - if$ - pages empty$ - 'skip$ - { duplicate$ empty$ - { pop$ format.pages } - { ",~" * pages n.dashify * } - if$ - } - if$ -} - -FUNCTION {format.chapter.pages} -{ chapter empty$ - 'format.pages - { type empty$ - { "chapter" } - { type "l" change.case$ } - if$ - chapter tie.or.space.connect - pages empty$ - 'skip$ - { ", " * format.pages * } - if$ - } - if$ -} - -FUNCTION {format.in.ed.booktitle} -{ booktitle empty$ - { "" } - { editor empty$ - { edition empty$ - {"In " booktitle emphasize *} - {"In " booktitle emphasize * ", " * edition * " ed." *} - if$ - } - { edition empty$ - {"In " booktitle emphasize * "; " * format.editors * } - {"In " booktitle emphasize * ", " * edition * " ed." * "; " * format.editors * } - if$ - } - if$ - } - if$ -} - -FUNCTION {format.in.ed.booktitle.proc} -{ booktitle empty$ - { "" } - { editor empty$ - { edition empty$ - {"In Proceedings of the " booktitle *} - {"In Proceedings of the " booktitle * ", " * edition * " ed." *} - if$ - } - { edition empty$ - {"In Proceedings of the " booktitle * "; " * format.editors * } - {"In Proceedings of the " booktitle * ", " * edition * " ed." * "; " * format.editors * } - if$ - } - if$ - } - if$ -} - -FUNCTION {format.publisher.and.address} -{ publisher empty$ - {""} - { address empty$ - {publisher } - {publisher ": " * address *} - if$ - } - if$ -} - - - -FUNCTION {empty.misc.check} -{ author empty$ title empty$ howpublished empty$ - month empty$ year empty$ note empty$ - and and and and and - { "all relevant fields are empty in " cite$ * warning$ } - 'skip$ - if$ -} - -FUNCTION {format.thesis.type} -{ type empty$ - 'skip$ - { pop$ - type "t" change.case$ - } - if$ -} - -FUNCTION {format.tr.number} -{ type empty$ - { "Technical Report" } - 'type - if$ - number empty$ - { "t" change.case$ } - { number tie.or.space.connect } - if$ -} - -FUNCTION {format.article.crossref} -{ key empty$ - { journal empty$ - { "need key or journal for " cite$ * " to crossref " * crossref * - warning$ - "" - } - { "In \emph{" journal * "}" * } - if$ - } - { "In " } - if$ - " \citet{" * crossref * "}" * -} - - - -FUNCTION {format.book.crossref} -{ volume empty$ - { "empty volume in " cite$ * "'s crossref of " * crossref * warning$ - "In " - } - { "Vol." volume tie.or.space.connect - " of " * - } - if$ - editor empty$ - editor field.or.null author field.or.null = - or - { key empty$ - { series empty$ - { "need editor, key, or series for " cite$ * " to crossref " * - crossref * warning$ - "" * - } - { "{\em " * series * "\/}" * } - if$ - } - { key * } - if$ - } - { "" * } - if$ - " \cite{" * crossref * "}" * -} - -FUNCTION {format.incoll.inproc.crossref} -{ editor empty$ - editor field.or.null author field.or.null = - or - { key empty$ - { booktitle empty$ - { "need editor, key, or booktitle for " cite$ * " to crossref " * - crossref * warning$ - "" - } - { "In {\em " booktitle * "\/}" * } - if$ - } - { "In " key * } - if$ - } - { "In " * } - if$ - " \cite{" * crossref * "}" * -} - -FUNCTION {format.website} -{ url empty$ - { "" } - { "" url website * - urldate empty$ - {"there is url but no urldate in " cite$ * warning$} - { ", accessed on " * urldate *} - if$ - } - if$ -} - - -%% the following function is modified from kp.bst at http://arxiv.org/hypertex/bibstyles/ -FUNCTION {format.eprint} -{eprint empty$ - { ""} - {primaryClass empty$ - {" \href{http://xxx.lanl.gov/abs/" eprint * "}" * "{{\normalfont " * "[" * eprint * "]" * "}}" *} - {archivePrefix empty$ - {" \href{http://xxx.lanl.gov/abs/" eprint * "}" * "{{\normalfont " * "[" * "arXiv:" * primaryClass * "/" * eprint * "]" * "}}" *} - {" \href{http://xxx.lanl.gov/abs/" eprint * "}" * "{{\normalfont " * "[" * archivePrefix * ":" * primaryClass * "/" * eprint * "]" * "}}" *} - if$ - } - if$ - } -if$ -} - - -%% For printing DOI numbers (it is a hyperlink but printed in black) -FUNCTION {formatfull.doi} -{ doi empty$ - { "" } - {"{\url{https://doi.org/" doi * "}}" * } - if$ -} - - - -FUNCTION {article} -{ output.bibitem - format.authors "author" output.check - author format.key output - new.block - format.title "title" output.check - new.block - crossref missing$ - { journal emphasize "journal" output.check - format.date * format.vol.num.pages "" * output - } - { format.article.crossref output.nonnull - format.pages output - } - if$ -format.eprint output -new.block -note output -formatfull.doi output -fin.entry -} - -FUNCTION {book} -{ output.bibitem - author empty$ - { format.editors "author and editor" output.check } - { format.authors output.nonnull - crossref missing$ - { "author and editor" editor either.or.check } - 'skip$ - if$ - } - if$ - new.block - format.btitle "title" output.check - format.edition output - after.item 'output.state := - crossref missing$ - { format.bvolume output - format.number.series output - format.publisher.and.address "publisher" output.check -%%% address output - } - { - format.book.crossref output.nonnull - } - if$ - format.bdate "year" output.check - after.item 'output.state := - format.chapter.pages output - format.eprint output - new.block - note output - formatfull.doi output - fin.entry -} - -FUNCTION {booklet} -{ output.bibitem - format.authors output - new.block - format.title "title" output.check - howpublished address new.block.checkb - howpublished output - address output - format.bdate output - format.eprint output - new.block - note output - formatfull.doi output - fin.entry -} - -FUNCTION {inbook} -{ output.bibitem - author empty$ - { format.editors "author and editor" output.check } - { format.authors output.nonnull - crossref missing$ - { "author and editor" editor either.or.check } - 'skip$ - if$ - } - if$ -%%% new.block - format.title "title" output.check - new.block - crossref missing$ - { format.in.ed.booktitle "booktitle" output.check - after.item 'output.state := - format.number.series output -%% new.sentence - format.publisher.and.address "publisher" output.check - format.bdate "year" output.check - after.item 'output.state := - format.bvolume output - format.chapter.pages "chapter and pages" output.check - - } - { format.chapter.pages "chapter and pages" output.check - new.block - format.book.crossref output.nonnull - format.bdate "year" output.check - } - if$ - format.eprint output - new.block - note output - formatfull.doi output - fin.entry -} - -FUNCTION {incollection} -{ output.bibitem - format.authors "author" output.check - new.block - format.title "title" output.check - new.sentence - crossref missing$ - { format.in.ed.booktitle "booktitle" output.check - after.item 'output.state := - format.number.series output -% new.sentence - format.publisher.and.address "publisher" output.check - format.bdate "year" output.check - after.item 'output.state := - format.bvolume output - format.chapter.pages output - } - { format.incoll.inproc.crossref output.nonnull - format.chapter.pages output - } - if$ - format.eprint output - new.block - note output - formatfull.doi output - fin.entry -} - -FUNCTION {inproceedings} -{ output.bibitem - format.authors "author" output.check - new.block - format.title "title" output.check - new.block - crossref missing$ - { format.in.ed.booktitle.proc "booktitle" output.check - address empty$ - { organization publisher new.sentence.checkb - organization output - publisher output - format.bdate "year" output.check - } - { after.item 'output.state := - organization output - format.publisher.and.address output.nonnull - format.bdate "year" output.check - after.item 'output.state := - } - if$ - format.number.series output - format.bvolume output - format.pages output - } - { format.incoll.inproc.crossref output.nonnull - format.pages output - } - if$ - format.eprint output - new.block - note output - formatfull.doi output - fin.entry -} - -FUNCTION {conference} { inproceedings } - -FUNCTION {manual} -{ output.bibitem - author empty$ - { organization empty$ - 'skip$ - { organization output.nonnull - address output - } - if$ - } - { format.authors output.nonnull } - if$ - new.block - format.btitle "title" output.check - author empty$ - { organization empty$ - { address new.block.checka - address output - } - 'skip$ - if$ - } - { organization address new.block.checkb - organization output - address output - } - if$ - format.edition output - format.bdate output - format.eprint output - new.block - note output - formatfull.doi output - fin.entry -} - -FUNCTION {mastersthesis} -{ output.bibitem - format.authors "author" output.check - new.block - format.title "title" output.check - new.block - "Master's thesis" format.thesis.type output.nonnull - school "school" output.check - address output - format.bdate "year" output.check - format.eprint output - new.block - note output - formatfull.doi output - fin.entry -} - -FUNCTION {misc} -{ output.bibitem - format.authors output - title howpublished new.block.checkb - format.title output - howpublished new.block.checka - howpublished output - format.bdate output - format.eprint output - new.block - note output - formatfull.doi output - fin.entry - empty.misc.check -} - -FUNCTION {phdthesis} -{ output.bibitem - format.authors "author" output.check - new.block - format.title "title" output.check - new.block - "PhD thesis" format.thesis.type output.nonnull - school "school" output.check - address output - format.bdate "year" output.check - format.eprint output - new.block - note output - formatfull.doi output - fin.entry -} - -FUNCTION {proceedings} -{ output.bibitem - editor empty$ - { organization output } - { format.editors output.nonnull } - if$ - new.block - format.btitle "title" output.check - format.bvolume output - format.number.series output - address empty$ - { editor empty$ - { publisher new.sentence.checka } - { organization publisher new.sentence.checkb - organization output - } - if$ - publisher output - format.bdate "year" output.check - } - { address output.nonnull - format.bdate "year" output.check - new.sentence - editor empty$ - 'skip$ - { organization output } - if$ - publisher output - } - if$ - format.eprint output - new.block - note output - formatfull.doi output - fin.entry -} - -FUNCTION {techreport} -{ output.bibitem - format.authors "author" output.check - new.block - format.title "title" output.check - new.block - format.tr.number output.nonnull - institution "institution" output.check - address output - format.bdate "year" output.check - format.eprint output - new.block - note output - formatfull.doi output - fin.entry -} - -FUNCTION {unpublished} -{ output.bibitem - format.authors "author" output.check - new.block - format.title "title" output.check - format.eprint output - new.block - note output - formatfull.doi output - fin.entry -} - -FUNCTION {www} -{ output.bibitem - format.authors "author" output.checkwoa - new.block - format.title "title" output.check - new.block - format.website "url" output.check - format.eprint output - new.block - note output - formatfull.doi output - fin.entry -} - -FUNCTION {patent} -{ output.bibitem - format.authors "author" output.check - new.block - format.title "title" output.check - new.block - format.number.patent "number" output.check - mid.sentence 'output.state := - format.pdate "date" output.check - format.eprint output - new.block - note output - formatfull.doi output - fin.entry -} - -READ - -FUNCTION {sortify} -{ purify$ - "l" change.case$ -} - - -INTEGERS { len } - -FUNCTION {chop.word} -{ 's := - 'len := - s #1 len substring$ = - { s len #1 + global.max$ substring$ } - 's - if$ -} - - -FUNCTION {format.lab.names} -{ 's := - s #1 "{vv~}{ll}" format.name$ - s num.names$ duplicate$ - #2 > - { pop$ " \em{et~al.}" * } - { #2 < - 'skip$ - { s #2 "{ff }{vv }{ll}{ jj}" format.name$ "others" = - { " \em{et~al.}" * } - { " and " * s #2 "{vv~}{ll}" format.name$ * } - if$ - } - if$ - } - if$ -} - - -FUNCTION {author.key.label} -{ author empty$ - { key empty$ - { cite$ #1 #3 substring$ } - 'key - if$ - } - { author format.lab.names } - if$ -} - -FUNCTION {author.editor.key.label} -{ author empty$ - { editor empty$ - { key empty$ - { cite$ #1 #3 substring$ } - 'key - if$ - } - { editor format.lab.names } - if$ - } - { author format.lab.names } - if$ -} - -FUNCTION {author.key.organization.label} -{ author empty$ - { key empty$ - { organization empty$ - { cite$ #1 #3 substring$ } - { "The " #4 organization chop.word #3 text.prefix$ } - if$ - } - 'key - if$ - } - { author format.lab.names } - if$ -} - -FUNCTION {editor.key.organization.label} -{ editor empty$ - { key empty$ - { organization empty$ - { cite$ #1 #3 substring$ } - { "The " #4 organization chop.word #3 text.prefix$ } - if$ - } - 'key - if$ - } - { editor format.lab.names } - if$ -} - -FUNCTION {calc.short.authors} -{ type$ "book" = - type$ "inbook" = - or - 'author.editor.key.label - { type$ "proceedings" = - 'editor.key.organization.label - { type$ "manual" = - 'author.key.organization.label - 'author.key.label - if$ - } - if$ - } - if$ - 'short.list := -} - -FUNCTION {calc.label} -{ calc.short.authors - short.list - "(" - * - year duplicate$ empty$ - short.list key field.or.null = or - { pop$ "" } - 'skip$ - if$ - * - 'label := -} - -INTEGERS { seq.num } - -FUNCTION {init.seq} -{ #0 'seq.num :=} - -EXECUTE {init.seq} - -FUNCTION {int.to.fix} -{ "000000000" swap$ int.to.str$ * - #-1 #10 substring$ -} - - -FUNCTION {presort} -{ calc.label - label sortify - " " - * - seq.num #1 + 'seq.num := - seq.num int.to.fix - 'sort.label := - sort.label * - #1 entry.max$ substring$ - 'sort.key$ := -} - -ITERATE {presort} - - -STRINGS { longest.label last.label next.extra } - -INTEGERS { longest.label.width last.extra.num number.label } - -FUNCTION {initialize.longest.label} -{ "" 'longest.label := - #0 int.to.chr$ 'last.label := - "" 'next.extra := - #0 'longest.label.width := - #0 'last.extra.num := - #0 'number.label := -} - -FUNCTION {forward.pass} -{ last.label label = - { last.extra.num #1 + 'last.extra.num := - last.extra.num int.to.chr$ 'extra.label := - } - { "a" chr.to.int$ 'last.extra.num := - "" 'extra.label := - label 'last.label := - } - if$ - number.label #1 + 'number.label := -} - -FUNCTION {reverse.pass} -{ next.extra "b" = - { "a" 'extra.label := } - 'skip$ - if$ - extra.label 'next.extra := - extra.label - duplicate$ empty$ - 'skip$ - { "{\natexlab{" swap$ * "}}" * } - if$ - 'extra.label := - label extra.label * 'label := -} - -EXECUTE {initialize.longest.label} - -ITERATE {forward.pass} - -REVERSE {reverse.pass} - -FUNCTION {begin.bib} -{ "\begin{thebibliography}{999}" - write$ newline$ -} - -EXECUTE {begin.bib} - -EXECUTE {init.state.consts} - -ITERATE {call.type$} - -FUNCTION {end.bib} -{ newline$ - "\end{thebibliography}" write$ newline$ -} - -EXECUTE {end.bib} - - diff --git a/papers/Mathematics/mdpi.cls b/papers/Mathematics/mdpi.cls deleted file mode 100644 index aad304f8c..000000000 --- a/papers/Mathematics/mdpi.cls +++ /dev/null @@ -1,1176 +0,0 @@ -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% %% MDPI class for LaTeX files 15.2.2019 b -%% %% For any information please send an e-mail to: -%% %% latex@mdpi.com -%% %% -%% %% Initial class provided by: -%% %% Stefano Mariani -%% %% Modified by: -%% %% Dietrich Rordorf -%% %% Peter Harremoes -%% %% Zeno Schumacher -%% %% Maddalena Giulini -%% %% Andres Gartmann -%% %% Dr. Janine Daum -%% %% Versions: -%% %% v1.0 before Dr. Janine Daum -%% %% v2.0 when Dr. Janine Daum started (March 2013) -%% %% v3.0 after layout change (September 2015) -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -%% IDENTIFICATION -\NeedsTeXFormat{LaTeX2e} -\ProvidesClass{mdpi}[15/02/2019 MDPI paper class] - -%%%% Copyright and citebox - \AtEndDocument{\par \cright} - -%% PRELIMINARY DECLARATIONS -\LoadClass[10pt,a4paper]{article} -\RequirePackage[T1]{fontenc} -\RequirePackage[utf8]{inputenc} -\RequirePackage{calc} -\RequirePackage{indentfirst} -\RequirePackage{fancyhdr} -\RequirePackage{graphicx,epstopdf} -\RequirePackage{lastpage} -\RequirePackage{ifthen} -\RequirePackage{float} -\RequirePackage{amsmath} -% TODO: Currently lineno needs to be loaded after amsmath because of conflict -% https://github.com/latex-lineno/lineno/issues/5 -\RequirePackage{lineno} -\RequirePackage{setspace} -\RequirePackage{enumitem} -\RequirePackage{mathpazo} -\RequirePackage{booktabs} % For \toprule etc. in tables -\RequirePackage[largestsep]{titlesec} -\RequirePackage{etoolbox} % For \AtBeginDocument etc. -\RequirePackage{tabto} % To use tab for alignment on first page -\RequirePackage[table]{xcolor} % To provide color for soul (for english editing) and provide coloring for tables (author request) -\RequirePackage{soul} % To highlight text -\newcommand{\highlight}[1]{\colorbox{yellow}{#1}} -\RequirePackage{multirow} -\RequirePackage{microtype} % For command \textls[]{} -\RequirePackage{tikz} % For \foreach used for Orcid icon -\RequirePackage{totcount} % To enable extracting the value of the counter "page" - - -%% OPTIONS -%% To choose the journal -% All journals (website name, full name, short name, DOI abbreviation, and ISSN) are defined in an extra file. -% This is the same as for mdpi.cls. -\input{journalnames} -\DeclareOption{journal}{\ClassWarning{mdpi}{You used an invalid journal name or you have not specified the journal. The first option of the documentclass command specifies the journal. The word 'journal' should be replaced by one of the journal names specified in template.tex (in the comment 'Choose between the following MDPI journal').}} - -%% To choose the type of manuscript -\DeclareOption{abstract}{\gdef\@arttype{Abstract}} -\DeclareOption{addendum}{\gdef\@arttype{Addendum}} -\DeclareOption{article}{\gdef\@arttype{Article}} -\DeclareOption{benchmark}{\gdef\@arttype{Benchmark}} -\DeclareOption{book}{\gdef\@arttype{Book}} -\DeclareOption{bookreview}{\gdef\@arttype{Book Review}} -\DeclareOption{briefreport}{\gdef\@arttype{Brief Report}} -\DeclareOption{casereport}{\gdef\@arttype{Case Report}} -\DeclareOption{changes}{\gdef\@arttype{Changes}} -\DeclareOption{comment}{\gdef\@arttype{Comment}} -\DeclareOption{commentary}{\gdef\@arttype{Commentary}} -\DeclareOption{communication}{\gdef\@arttype{Communication}} -\DeclareOption{conceptpaper}{\gdef\@arttype{Concept Paper}} -\DeclareOption{conferenceproceedings}{\gdef\@arttype{Proceedings}} -\DeclareOption{correction}{\gdef\@arttype{Correction}} -\DeclareOption{conferencereport}{\gdef\@arttype{Conference Report}} -\DeclareOption{expressionofconcern}{\gdef\@arttype{Expression of Concern}} -\DeclareOption{extendedabstract}{\gdef\@arttype{Extended Abstract}} -\DeclareOption{meetingreport}{\gdef\@arttype{Meeting Report}} -\DeclareOption{creative}{\gdef\@arttype{Creative}} -\DeclareOption{datadescriptor}{\gdef\@arttype{Data Descriptor}} -\DeclareOption{discussion}{\gdef\@arttype{Discussion}} -\DeclareOption{editorial}{\gdef\@arttype{Editorial}} -\DeclareOption{essay}{\gdef\@arttype{Essay}} -\DeclareOption{erratum}{\gdef\@arttype{Erratum}} -\DeclareOption{hypothesis}{\gdef\@arttype{Hypothesis}} -\DeclareOption{interestingimages}{\gdef\@arttype{Interesting Images}} -\DeclareOption{letter}{\gdef\@arttype{Letter}} -\DeclareOption{meetingreport}{\gdef\@arttype{Meeting Report}} -\DeclareOption{newbookreceived}{\gdef\@arttype{New Book Received}} -\DeclareOption{obituary}{\gdef\@arttype{Obituary}} -\DeclareOption{opinion}{\gdef\@arttype{Opinion}} -\DeclareOption{projectreport}{\gdef\@arttype{Project Report}} -\DeclareOption{reply}{\gdef\@arttype{Reply}} -\DeclareOption{retraction}{\gdef\@arttype{Retraction}} -\DeclareOption{review}{\gdef\@arttype{Review}} -\DeclareOption{perspective}{\gdef\@arttype{Perspective}} -\DeclareOption{protocol}{\gdef\@arttype{Protocol}} -\DeclareOption{shortnote}{\gdef\@arttype{Short Note}} -\DeclareOption{supfile}{\gdef\@arttype{Supfile}} -\DeclareOption{technicalnote}{\gdef\@arttype{Technical Note}} -\DeclareOption{viewpoint}{\gdef\@arttype{Viewpoint}} - -%% To choose the status of the manuscript -\DeclareOption{submit}{\gdef\@status{submit}} -\DeclareOption{accept}{\gdef\@status{accept}} - -%% To choose the whether there is one or more authors -\DeclareOption{oneauthor}{\gdef\@authornum{author}} -\DeclareOption{moreauthors}{\gdef\@authornum{authors}} - -%% Add the chosen options to the class -\DeclareOption*{\PassOptionsToClass{\CurrentOption}{article}} - -%% Defaults -\ExecuteOptions{notspecified,10pt,a4paper,article,submit,oneauthor} - -%% Process options -\ProcessOptions\relax - -%% MORE DECLARATIONS -%%%% Maths environments -\RequirePackage{amsthm} -\newtheoremstyle{mdpi}% name -{12pt}% space above -{12pt}% space below -{\itshape}% body font -{}% indent amount 1 -{\bfseries}% theorem head font -{.}% punctuation after theorem head -{.5em}% space after theorem head -{}% theorem head spec (can be left empty, meaning `normal') - -\renewcommand{\qed}{\unskip\nobreak\quad\qedsymbol} %% This places the symbol right after the text instead of placing it at the end on the line. - -\renewenvironment{proof}[1][\proofname]{\par %% \proofname allows to have "Proof of my theorem" - \pushQED{\qed}% - \normalfont \topsep6\p@\@plus6\p@\relax - \trivlist - \item[\hskip\labelsep - \bfseries %% "Proof" is bold - #1\@addpunct{.}]\ignorespaces %% Period instead of colon -}{% - \popQED\endtrivlist\@endpefalse -} - - \theoremstyle{mdpi} - \newcounter{theorem} - \setcounter{theorem}{0} - \newtheorem{Theorem}[theorem]{Theorem} - - \newcounter{lemma} - \setcounter{lemma}{0} - \newtheorem{Lemma}[lemma]{Lemma} - - \newcounter{corollary} - \setcounter{corollary}{0} - \newtheorem{Corollary}[corollary]{Corollary} - - \newcounter{proposition} - \setcounter{proposition}{0} - \newtheorem{Proposition}[proposition]{Proposition} - - \newcounter{characterization} - \setcounter{characterization}{0} - \newtheorem{Characterization}[characterization]{Characterization} - - \newcounter{property} - \setcounter{property}{0} - \newtheorem{Property}[property]{Property} - - \newcounter{problem} - \setcounter{problem}{0} - \newtheorem{Problem}[problem]{Problem} - - \newcounter{example} - \setcounter{example}{0} - \newtheorem{Example}[example]{Example} - - \newcounter{examplesanddefinitions} - \setcounter{examplesanddefinitions}{0} - \newtheorem{ExamplesandDefinitions}[examplesanddefinitions]{Examples and Definitions} - - \newcounter{remark} - \setcounter{remark}{0} - \newtheorem{Remark}[remark]{Remark} - - \newcounter{definition} - \setcounter{definition}{0} - \newtheorem{Definition}[definition]{Definition} - - \newcounter{hypothesis} - \setcounter{hypothesis}{0} - \newtheorem{Hypothesis}[hypothesis]{Hypothesis} - - \newcounter{notation} - \setcounter{notation}{0} - \newtheorem{Notation}[notation]{Notation} - -%%%% Hyphenation -\RequirePackage[none]{hyphenat} -\sloppy - -%%%% References -\RequirePackage[sort&compress,sectionbib]{natbib} % option sectionbib is for optionally organizing references using sections (author request) - -\ifthenelse{\equal{\@journal}{admsci} -\OR \equal{\@journal}{arts} -\OR \equal{\@journal}{econometrics} -\OR \equal{\@journal}{economies} -\OR \equal{\@journal}{genealogy} -\OR \equal{\@journal}{humanities} -\OR \equal{\@journal}{ijfs} -\OR \equal{\@journal}{jrfm} -\OR \equal{\@journal}{languages} -\OR \equal{\@journal}{laws} -\OR \equal{\@journal}{religions} -\OR \equal{\@journal}{risks} -\OR \equal{\@journal}{socsci}}{% - \bibliographystyle{chicago2} - \bibpunct{(}{)}{;}{x}{}{}% - }{% - \bibliographystyle{mdpi} - \bibpunct{[}{]}{,}{n}{}{}% - }% - -\renewcommand\NAT@set@cites{% - \ifNAT@numbers - \ifNAT@super \let\@cite\NAT@citesuper - \def\NAT@mbox##1{\unskip\nobreak\textsuperscript{##1}}% - \let\citeyearpar=\citeyear - \let\NAT@space\relax - \def\NAT@super@kern{\kern\p@}% - \else - \let\NAT@mbox=\mbox - \let\@cite\NAT@citenum - \let\NAT@space\relax - \let\NAT@super@kern\relax - \fi - \let\@citex\NAT@citexnum - \let\@biblabel\NAT@biblabelnum - \let\@bibsetup\NAT@bibsetnum - \renewcommand\NAT@idxtxt{\NAT@name\NAT@spacechar\NAT@open\NAT@num\NAT@close}% - \def\natexlab##1{}% - \def\NAT@penalty{\penalty\@m}% - \else - \let\@cite\NAT@cite - \let\@citex\NAT@citex - \let\@biblabel\NAT@biblabel - \let\@bibsetup\NAT@bibsetup - \let\NAT@space\NAT@spacechar - \let\NAT@penalty\@empty - \renewcommand\NAT@idxtxt{\NAT@name\NAT@spacechar\NAT@open\NAT@date\NAT@close}% - \def\natexlab##1{##1}% - \fi} - -%%%%% Hyperlinks -%% Define color for citations -\definecolor{bluecite}{HTML}{0875b7} - -\ifthenelse{\equal{\@arttype}{Book}}{ - \RequirePackage[unicode=true, - bookmarksopen={true}, - pdffitwindow=true, - colorlinks=true, - linkcolor=black, - citecolor=black, - urlcolor=black, - hyperfootnotes=false, - pdfstartview={FitH}, - pdfpagemode=UseNone]{hyperref} - }{ - \RequirePackage[unicode=true, - bookmarksopen={true}, - pdffitwindow=true, - colorlinks=true, - linkcolor=bluecite, - citecolor=bluecite, - urlcolor=bluecite, - hyperfootnotes=false, - pdfstartview={FitH}, - pdfpagemode= UseNone]{hyperref} -} - -%% To have the possibility to change the urlcolor -\newcommand{\changeurlcolor}[1]{\hypersetup{urlcolor=#1}} - -%% Metadata -\newcommand{\org@maketitle}{}% LATEX-Check -\let\org@maketitle\maketitle -\def\maketitle{% - \hypersetup{ - pdftitle={\@Title}, - pdfsubject={\@abstract}, - pdfkeywords={\@keyword}, - pdfauthor={\@AuthorNames} - }% - \org@maketitle -} - -%%%% Footnotes -\RequirePackage[hang]{footmisc} -\setlength{\skip\footins}{1.2cm} -\setlength{\footnotemargin}{5mm} -\def\footnoterule{\kern-14\p@ -\hrule \@width 2in \kern 11.6\p@} - -%%%% URL -\RequirePackage{url} -\urlstyle{same} -\g@addto@macro{\UrlBreaks}{\UrlOrds} - -%%%% Widows & orphans -\clubpenalty=10000 -\widowpenalty=10000 -\displaywidowpenalty=10000 - -%%%% Front matter -\newcommand{\firstargument}{} -\newcommand{\Title}[1]{\gdef\@Title{#1}}% -\newcommand{\Author}[1]{\gdef\@Author{#1}}% -\def\@AuthorNames{} -\newcommand{\AuthorNames}[1]{\gdef\@AuthorNames{#1}}% -\newcommand{\firstpage}[1]{\gdef\@firstpage{#1}} -\newcommand{\doinum}[1]{\gdef\@doinum{#1}} - -% DOI number -\newcommand\twodigits[1]{% -\ifnum#1<10 -0\number#1 - \else -\number#1 -\fi -} - -\newcommand\fourdigits[1]{% -\ifnum#1<10 000\number#1 - \else - \ifnum#1<100 00\number#1 - \else - \ifnum#1<1000 0\number#1 - \else - \ifnum#1<10000 \number#1 - \else - error - \fi - \fi - \fi - \fi -} - - -\ifthenelse{\equal{\@journal}{molbank}}{ - \doinum{10.3390/\@articlenumber} - }{ - \doinum{10.3390/\@doiabbr\@pubvolume\twodigits\@issuenum\fourdigits\@articlenumber} -} - - -\newcommand{\pubvolume}[1]{\gdef\@pubvolume{#1}} -\newcommand{\pubyear}[1]{\gdef\@pubyear{#1}} -\newcommand{\copyrightyear}[1]{\gdef\@copyrightyear{#1}} -\newcommand{\address}[2][]{\renewcommand{\firstargument}{#1}\gdef\@address{#2}} -\newcommand{\corresfirstargument}{} -\def\@corres{} -\newcommand{\corres}[2][]{\renewcommand{\corresfirstargument}{#1}\gdef\@corres{#2}} -\def\@conference{} -\newcommand{\conference}[1]{\gdef\@conference{#1}}% -\def\@abstract{} -\renewcommand{\abstract}[1]{\gdef\@abstract{#1}} -\def\@externaleditor{} -\newcommand{\externaleditor}[1]{\gdef\@externaleditor{#1}} -\def\@LSID{} -\newcommand{\LSID}[1]{\gdef\@LSID{#1}} -\newcommand{\history}[1]{\gdef\@history{#1}} -\def\@pacs{} -\newcommand{\PACS}[1]{\gdef\@pacs{#1}} -\def\@msc{} -\newcommand{\MSC}[1]{\gdef\@msc{#1}} -\def\@jel{} -\newcommand{\JEL}[1]{\gdef\@jel{#1}} -\def\@keyword{} -\newcommand{\keyword}[1]{\gdef\@keyword{#1}} -\def\@dataset{} -\newcommand{\dataset}[1]{\gdef\@dataset{#1}} -\def\@datasetlicense{} -\newcommand{\datasetlicense}[1]{\gdef\@datasetlicense{#1}} -\def\@featuredapplication{} -\newcommand{\featuredapplication}[1]{\gdef\@featuredapplication{#1}} -\def\@keycontribution{} -\newcommand{\keycontribution}[1]{\gdef\@keycontribution{#1}} - - -\def\@issuenum{} -\newcommand{\issuenum}[1]{\gdef\@issuenum{#1}} -\def\@updates{} -\newcommand{\updates}[1]{\gdef\@updates{#1}} - -\def\@firstnote{} -\newcommand{\firstnote}[1]{\gdef\@firstnote{#1}} -\def\@secondnote{} -\newcommand{\secondnote}[1]{\gdef\@secondnote{#1}}% -\def\@thirdnote{} -\newcommand{\thirdnote}[1]{\gdef\@thirdnote{#1}}% -\def\@fourthnote{} -\newcommand{\fourthnote}[1]{\gdef\@fourthnote{#1}}% -\def\@fifthnote{} -\newcommand{\fifthnote}[1]{\gdef\@fifthnote{#1}}% -\def\@sixthnote{} -\newcommand{\sixthnote}[1]{\gdef\@sixthnote{#1}}% -\def\@seventhnote{} -\newcommand{\seventhnote}[1]{\gdef\@seventhnote{#1}}% -\def\@eighthnote{} -\newcommand{\eighthnote}[1]{\gdef\@eighthnote{#1}}% - -\def\@simplesumm{} -\newcommand{\simplesumm}[1]{\gdef\@simplesumm{#1}} -\newcommand{\articlenumber}[1]{\gdef\@articlenumber{#1}} - -\def\@externalbibliography{} -\newcommand{\externalbibliography}[1]{\gdef\@externalbibliography{#1}} - -\def\@reftitle{} -\newcommand{\reftitle}[1]{\gdef\@reftitle{#1}} - -% For transition period to change back to continuous page numbers -\def\@continuouspages{} -\newcommand{\continuouspages}[1]{\gdef\@continuouspages{#1}} - - -%% ORCID -% Make Orcid icon -\newcommand{\orcidicon}{\includegraphics[width=0.32cm]{logo-orcid.pdf}} - -% Define link and button for each author -\foreach \x in {A, ..., Z}{% -\expandafter\xdef\csname orcid\x\endcsname{\noexpand\href{https://orcid.org/\csname orcidauthor\x\endcsname}{\noexpand\orcidicon}} -} - -%%%% Journal name for the header -\newcommand{\journalname}{\@journalshort} - - -\regtotcounter{page} % to enable extracting the value of the counter "page" using the totcount package - -%%%% Header and footer on first page -%% The plain page style needs to be redefined because with \maketitle in the article class, LaTeX applies the the plain page style automatically to the first page. -\ifthenelse{\equal{\@journal}{preprints} % - \OR \equal{\@arttype}{Book}}{% - \fancypagestyle{plain}{% - \fancyhf{} - \ifthenelse{\equal{\@arttype}{Book}}{ - 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author = {Christophe Leys and Christophe Ley and Olivier Klein and Philippe Bernard and Laurent Licata}, - journal = {Journal of Experimental Social Psychology}, - volume = {49}, - number = {4}, - pages = {764-766}, - year = {2013}, - doi = {10.1016/j.jesp.2013.03.013}, - url = {https://doi.org/10.1016/j.jesp.2013.03.013} -} - -@article{leys2018outliers, - title = {Detecting multivariate outliers: Use a robust variant of the Mahalanobis distance}, - journal = {Journal of Experimental Social Psychology}, - volume = {74}, - pages = {150-156}, - year = {2018}, - issn = {0022-1031}, - doi = {10.1016/j.jesp.2017.09.011}, - url = {https://www.sciencedirect.com/science/article/pii/S0022103117302123}, - author = {Christophe Leys and Olivier Klein and Yves Dominicy and Christophe Ley}, -} - -@article{simmons2011false, - author = {Joseph P. Simmons and Leif D. Nelson and Uri Simonsohn}, - title ={False-Positive Psychology: Undisclosed Flexibility in Data Collection and Analysis Allows Presenting Anything as Significant}, - journal = {Psychological Science}, - volume = {22}, - number = {11}, - pages = {1359-1366}, - year = {2011}, - doi = {10.1177/0956797611417632}, - URL = {https://doi.org/10.1177/0956797611417632}, -} - -@Article{easystatspackage, - title = {easystats: Framework for Easy Statistical Modeling, Visualization, and Reporting}, - author = {Daniel Lüdecke and Mattan S. Ben-Shachar and Indrajeet Patil and Brenton M. Wiernik and Etienne Bacher and Rémi Thériault and Dominique Makowski}, - journal = {CRAN}, - year = {2022}, - note = {R package}, - url = {https://easystats.github.io/easystats/}, - } - -@Article{ludecke2021performance, - author = {Daniel Lüdecke and Mattan S. Ben-Shachar and Indrajeet Patil and Philip Waggoner and Dominique Makowski}, - title = {{performance}: An R package for assessment, comparison and testing of statistical models}, - volume = {6}, - number = {60}, - journal = {Journal of Open Source Software}, - year = {2021}, - pages = {3139}, - doi = {10.21105/joss.03139}, - url = {https://doi.org/10.21105/joss.03139} - } - -@Article{patil2022datawizard, - title = {{datawizard}: An {R} package for easy data preparation and statistical transformations}, - author = {Indrajeet Patil and Dominique Makowski and Mattan S. Ben-Shachar and Brenton M. Wiernik and Etienne Bacher and Daniel Lüdecke}, - journal = {Journal of Open Source Software}, - year = {2022}, - volume = {7}, - number = {78}, - pages = {4684}, - doi = {10.21105/joss.04684}, - } - -@article{cook1977detection, - author = {R. Dennis Cook}, - title = {Detection of Influential Observation in Linear Regression}, - journal = {Technometrics}, - volume = {19}, - number = {1}, - pages = {15-18}, - year = {1977}, - publisher = {Taylor & Francis}, - doi = {10.1080/00401706.1977.10489493} -} - -@book{iglewicz1993outliers, - title = {How to detect and handle outliers (Vol. 16)}, - publisher = {Asq Press}, - author = {Iglewicz, B. and Hoaglin, D. C}, - year = {1993} -} - -@article{gnanadesikan1972robust, - title = {Robust estimates, residuals, and outlier detection with multiresponse data}, - author = {Gnanadesikan, R. and Kettenring, J. R}, - journal = {Biometrics}, - pages = {81-124}, - year = {1972} -} - -@article{hubert2018mcd, - author = {Hubert, Mia and Debruyne, Michiel and Rousseeuw, Peter J.}, - title = {Minimum covariance determinant and extensions}, - journal = {Wiley Interdisciplinary Reviews: Computational Statistics}, - volume = {10}, - number = {3}, - pages = {e1421}, - doi = {10.1002/wics.1421}, - url = {https://doi.org/10.1002/wics.1421}, - year = {2018} -} - -@article{tukey1963less, - title={Less vulnerable confidence and significance procedures for location based on a single sample: Trimming/Winsorization 1}, - author={Tukey, John W and McLaughlin, Donald H}, - journal={Sankhy{\=a}: The Indian Journal of Statistics, Series A}, - pages={331--352}, - year={1963}, - publisher={JSTOR} -} - -@article{van1995statistical, - title={Statistical mimicking of reaction time data: Single-process models, parameter variability, and mixtures}, - author={Van Zandt, Trisha and Ratcliff, Roger}, - journal={Psychonomic Bulletin \& Review}, - volume={2}, - number={1}, - pages={20--54}, - year={1995}, - publisher={Springer}, - doi = {10.3758/BF03214411} -} - -@article{ratcliff1993methods, - title={Methods for dealing with reaction time outliers.}, - author={Ratcliff, Roger}, - journal={Psychological bulletin}, - volume={114}, - number={3}, - pages={510}, - year={1993}, - publisher={American Psychological Association}, - doi = {10.1037/0033-2909.114.3.510} -} - -@book{mcelreath2020statistical, - title={Statistical rethinking: A Bayesian course with examples in R and Stan}, - author={McElreath, Richard}, - year={2020}, - publisher={CRC press} -} - -@Manual{rcore, - title = {{R}: A Language and Environment for Statistical Computing}, - author = {{R Core Team}}, - organization = {R Foundation for Statistical Computing}, - address = {Vienna, Austria}, - year = {2021}, - url = {https://www.R-project.org/} -} \ No newline at end of file diff --git a/papers/Mathematics/paper.Rmd b/papers/Mathematics/paper.Rmd deleted file mode 100644 index e35b6f02b..000000000 --- a/papers/Mathematics/paper.Rmd +++ /dev/null @@ -1,310 +0,0 @@ ---- -title: "Check your outliers! An introduction to identifying statistical outliers in R with *easystats*" -author: - - name: Rémi Thériault - affil: 1,* - orcid: 0000-0003-4315-6788 - - name: Mattan S. Ben-Shachar - affil: 2 - orcid: 0000-0002-4287-4801 - - name: Indrajeet Patil - affil: 3 - orcid: 0000-0003-1995-6531 - - name: Daniel Lüdecke - affil: 4 - orcid: 0000-0002-8895-3206 - - name: Brenton M. Wiernik - affil: 5 - orcid: 0000-0001-9560-6336 - - name: Dominique Makowski - affil: 6 - orcid: 0000-0001-5375-9967 -affiliation: - - num: 1 - address: Department of Psychology, Université du Québec à Montréal, Montréal, Québec, Canada - - num: 2 - address: Independent Researcher - - num: 3 - address: Center for Humans and Machines, Max Planck Institute for Human Development, Berlin, Germany - - num: 4 - address: Institute of Medical Sociology, University Medical Center Hamburg-Eppendorf, Germany - - num: 5 - address: Independent Researcher, Tampa, FL, USA - - num: 6 - address: School of Psychology, University of Sussex, Brighton, UK -correspondence: theriault.remi@courrier.uqam.ca. -journal: "mathematics" -type: article -status: submit -bibliography: mybibfile.bib -simplesummary: | - The *{performance}* package from the *easystats* ecosystem makes it easy to - diagnose outliers in R and according to current best practices thanks to the - `check_outiers()` function. -abstract: | - Beyond the challenge of keeping up-to-date with current best practices - regarding the diagnosis and treatment of outliers, an additional difficulty - arises concerning the mathematical implementation of the recommended methods. - In this paper, we provide an overview of current recommandations and best - practices and demonstrate how they can easily and conveniently be - implemented in the R statistical computing software, using the *{performance}* - package of the *easystats* ecosystem. We cover univariate, multivariate, and - model-based statistical outlier detection methods, their recommended - threshold, standard output, and plotting methods. We conclude with - recommendations on the handling of outliers: the different theoretical types - of outliers, whether to exclude or winsorize them, and the importance of - transparency. -keywords: | - univariate outliers; multivariate outliers; robust detection methods; R; easystats -acknowledgement: | - *{performance}* is part of the collaborative - [*easystats*](https://github.com/easystats/easystats) ecosystem - [@easystatspackage]. Thus, we thank all - [members of easystats](https://github.com/orgs/easystats/people), - contributors, and users alike. -authorcontributions: | - R.T. drafted the paper; all authors contributed to both the writing of the - paper and the conception of the software. -funding: | - This research received no external funding. -conflictsofinterest: | - The authors declare no conflict of interest. -abbreviations: - - short: SOD - long: Statistical outlier detection - - short: SEM - long: Structural equation modelling - - short: SD - long: Standard deviation - - short: MAD - long: Median absolute deviation - - short: IQR - long: Interquartile range - - short: HDI - long: Highest density interval - - short: BCI - long: Bias corrected and accelerated interval - - short: MCD - long: Minimum covariance determinant - - short: ICS - long: invariant coordinate selection - - short: OSF - long: Open Science Framework -output: rticles::mdpi_article ---- - -```{r setup, include=FALSE} -knitr::opts_chunk$set( - echo = TRUE, - comment = "#>", - out.width = "100%", - dpi = 300, - warning = FALSE -) - -library(performance) -library(see) -library(datawizard) -``` - -# Introduction - -Real-life data often contain observations that can be considered *abnormal* when compared to the main population. The cause of it---be it because they belong to a different distribution (originating from a different generative process) or simply being extreme cases, statistically rare but not impossible---can be hard to assess, and the boundaries of "abnormal" are hard to define. - -Nonetheless, the improper handling of these outliers can substantially affect statistical model estimations, biasing effect estimations and weakening the models' predictive performance. -It is thus essential to address this problem in a thoughtful manner. Yet, despite the existence of established recommendations and guidelines, many researchers still do not treat outliers in a consistent manner, or do so using inappropriate strategies [@simmons2011false; @leys2013outliers]. - -One possible reason is that researchers are not aware of the existing recommendations, or do not know how to implement them using their analysis software. In this paper, we show how to follow current best practices for automatic and reproducible statistical outlier detection (SOD) using R and the *{performance}* package [@ludecke2021performance], which is part of the *easystats* ecosystem of packages that build an R framework for easy statistical modeling, visualization, and reporting [@easystatspackage]. - -# Identifying Outliers - -Although many researchers attempt to identify outliers with measures based on the mean (e.g., _z_ scores), those methods are problematic because the mean and standard deviation themselves are not robust to the influence of outliers and they assume normally distributed data (i.e., a Gaussian distribution). Therefore, current guidelines recommend using robust methods to identify outliers, such as those relying on the median as opposed to the mean [@leys2019outliers; @leys2013outliers; @leys2018outliers]. - -Nonetheless, which exact outlier method to use depends on many factors. In some cases, eye-gauging odd observations can be an appropriate solution, though many researchers will favour algorithmic solutions to detect potential outliers, for example, based on a continuous value expressing the observation stands out from the others. - -One of the factors to consider when selecting an algorithmic outlier detection method is the statistical test of interest. When using a regression model, relevant information can be found by identifying observations that do not fit well with the model. This approach, known as model-based outliers detection (as outliers are extracted after the statistical model has been fit), can be contrasted with distribution-based outliers detection, which is based on the distance between an observation and the "center" of its population. Various quantification strategies of this distance exist for the latter, both univariate (involving only one variable at a time) or multivariate (involving multiple variables). - -When no method is readily available to detect model-based outliers, such as for structural equation modelling (SEM), looking for multivariate outliers may be of relevance. For simple tests (_t_ tests or correlations) that compare values of the same variable, it can be appropriate to check for univariate outliers. However, univariate methods can give false positives since _t_ tests and correlations, ultimately, are also models/multivariable statistics. They are in this sense more limited, but we show them nonetheless for educational purposes. - -Importantly, whatever approach researchers choose remains a subjective decision, which usage (and rationale) must be transparently documented and reproducible [@leys2019outliers]. Researchers should commit (ideally in a preregistration) to an outlier treatment method before collecting the data. They should report in the paper their decisions and details of their methods, as well as any deviation from their original plan. These transparency practices can help reduce false positives due to excessive researchers' degrees of freedom (i.e., choice flexibility throughout the analysis). In the following section, we will go through each of the mentioned methods and provide examples on how to implement them with R. - -## Univariate Outliers - -Researchers frequently attempt to identify outliers using measures of deviation from the center of a variable's distribution. One of the most popular such procedure is the _z_ score transformation, which computes the distance in standard deviation (SD) from the mean. However, as mentioned earlier, this popular method is not robust. Therefore, for univariate outliers, it is recommended to use the median along with the Median Absolute Deviation (MAD), which are more robust than the interquartile range or the mean and its standard deviation [@leys2019outliers; @leys2013outliers]. - -Researchers can identify outliers based on robust (i.e., MAD-based) _z_ scores using the `check_outliers()` function of the *{performance}* package, by specifying `method = "zscore_robust"`.^[Note that `check_outliers()` only checks numeric variables.] Although @leys2013outliers suggest a default threshold of 2.5 and @leys2019outliers a threshold of 3, *{performance}* uses by default a less conservative threshold of ~3.29.^[3.29 is an approximation of the two-tailed critical value for _p_ < .001, obtained through `qnorm(p = 1 - 0.001 / 2)`. We chose this threshold for consistency with the thresholds of all our other methods.] That is, data points will be flagged as outliers if they go beyond +/- ~3.29 MAD. Users can adjust this threshold using the `threshold` argument, as demonstrated below. - -```{r z_score} -library(performance) - -# Create some artificial outliers and an ID column -data <- rbind(mtcars[1:4], 42, 55) -data <- cbind(car = row.names(data), data) - -outliers <- check_outliers(data, method = "zscore_robust", ID = "car") -outliers -``` - -The row numbers of the detected outliers can be obtained by using `which()` on the output object, which can be used for exclusions for example: - -```{r} -which(outliers) - -data_clean <- data[-which(outliers), ] -``` - -All `check_outliers()` output objects possess a `plot()` method, meaning it is also possible to visualize the outliers: - -```{r univariate, fig.cap = "Visual depiction of outliers using the robust z-score method."} -library(see) - -plot(outliers) -``` - -Other univariate methods are available, such as using the interquartile range (IQR), or based on different intervals, such as the Highest Density Interval (HDI) or the Bias Corrected and Accelerated Interval (BCI). These methods are documented and described in the function's [help page](). - -## Multivariate Outliers - -Univariate outliers can be useful when the focus is on a particular variable, for instance the reaction time, as extreme values might be indicative of inattention or non-task-related behavior^[ Note that they might not be the optimal way of treating reaction time outliers [@ratcliff1993methods; @van1995statistical]]. - -However, in many scenarios, variables of a data set are not independent, and an abnormal observation will impact multiple dimensions. For instance, a participant giving random answers to a questionnaire. In this case, computing the _z_ score for each of the questions might not lead to satisfactory results. Instead, one might want to look at these variables together. - -One common approach for this is to compute multivariate distance metrics such as the Mahalanobis distance. Although the Mahalanobis distance is very popular, just like the regular _z_ scores method, it is not robust and is heavily influenced by the outliers themselves. Therefore, for multivariate outliers, it is recommended to use the Minimum Covariance Determinant, a robust version of the Mahalanobis distance [MCD, @leys2018outliers; @leys2019outliers]. - -In *{performance}*'s `check_outliers()`, one can use this approach with `method = "mcd"`.^[Our default threshold for the MCD method is defined by `stats::qchisq(p = 1 - 0.001, df = ncol(x))`, which again is an approximation of the critical value for _p_ < .001 consistent with the thresholds of our other methods.] - -```{r multivariate, fig.cap = "Visual depiction of outliers using the Minimum Covariance Determinant (MCD) method, a robust version of the Mahalanobis distance."} -outliers <- check_outliers(data, method = "mcd") -outliers - -plot(outliers) -``` - -Other multivariate methods are available, such as another type of robust Mahalanobis distance that in this case relies on an orthogonalized Gnanadesikan-Kettenring pairwise estimator [@gnanadesikan1972robust]. These methods are documented and described in the function's [help page](https://easystats.github.io/performance/reference/check_outliers.html). - -## Model-Based Outliers - -Working with regression models creates the possibility of using model-based SOD methods. These methods rely on the concept of *leverage*, that is, how much influence a given observation can have on the model estimates. If few observations have a relatively strong leverage/influence on the model, one can suspect that the model's estimates are biased by these observations, in which case flagging them as outliers could prove helpful (see next section, "Handling Outliers"). - -In {performance}, two such model-based SOD methods are currently available: Cook's distance, for regular regression models, and Pareto, for Bayesian models. As such, `check_outliers()` can be applied directly on regression model objects, by simply specifying `method = "cook"` (or `method = "pareto"` for Bayesian models).^[Our default threshold for the Cook method is defined by `stats::qf(0.5, ncol(x), nrow(x) - ncol(x))`, which again is an approximation of the critical value for _p_ < .001 consistent with the thresholds of our other methods.] - -```{r model, fig.cap = "Visual depiction of outliers based on Cook's distance (leverage and standardized residuals)."} -model <- lm(disp ~ mpg * disp, data = data) -outliers <- check_outliers(model, method = "cook") -outliers - -plot(outliers) -``` - -Table 1 below summarizes which methods to use in which cases, and with what threshold. - -```{r, echo=FALSE} -df <- data.frame( - `Statistical Test` = c( - "Supported regression model", - "Structural Equation Modeling (or other unsupported model)", - "Simple test with few variables (*t* test, correlation, etc.)"), - `Diagnosis Method` = c( - "**Model-based**: Cook (or Pareto for Bayesian models)", - "**Multivariate**: Minimum Covariance Determinant (MCD)", - "**Univariate**: robust *z* scores (MAD)"), - `Recommended Threshold` = c( - "`qf(0.5, ncol(x), nrow(x) - ncol(x))` (or 0.7 for Pareto)", - "`qchisq(p = 1 - 0.001, df = ncol(x))`", - "`qnorm(p = 1 - 0.001 / 2)`, ~ 3.29") -) -knitr::kable( - df, col.names = gsub("[.]", " ", names(df)), - caption = "Summary of Statistical Outlier Detection Methods Recommendations.", longtable = TRUE) -``` - -### Cook's Distance vs. MCD - -@leys2018outliers report a preference for the MCD method over Cook's distance. This is because Cook's distance removes one observation at a time and checks its corresponding influence on the model each time [@cook1977detection], and flags any observation that has a large influence. In the view of these authors, when there are several outliers, the process of removing a single outlier at a time is problematic as the model remains "contaminated" or influenced by other possible outliers in the model, rendering this method suboptimal in the presence of multiple outliers. - -However, distribution-based approaches are not a silver bullet either, and there are cases where the usage of methods agnostic to theoretical and statistical models of interest might be problematic. For example, a very tall person would be expected to also be much heavier than average, but that would still fit with the expected association between height and weight (i.e., it would be in line with a model such as `weight ~ height`). In contrast, using multivariate outlier detection methods there may flag this person as being an outlier---being unusual on two variables, height and weight---even though the pattern fits perfectly with our predictions. - -In the example below, we plot the raw data and see two possible outliers. The first one falls along the regression line, and is therefore "in line" with our hypothesis. The second one clearly diverges from the regression line, and therefore we can conclude that this outlier may have a disproportionate influence on our model. - -```{r scatter, fig.cap = "Scatter plot of height and weight, with two extreme observations: one model-consistent (top-right) and the other, model-inconsistent (i.e., an outlier; bottom-right)."} -data <- women[rep(seq_len(nrow(women)), each = 100), ] -data <- rbind(data, c(100, 258), c(100, 200)) -model <- lm(weight ~ height, data) -rempsyc::nice_scatter(data, "height", "weight") -``` - -Using either the *z*-score or MCD methods, our model-consistent observation will be incorrectly flagged as an outlier or influential observation. - -```{r} -outliers <- check_outliers(model, method = c("zscore_robust", "mcd")) -which(outliers) -``` - -In contrast, the model-based detection method displays the desired behaviour: it correctly flags the person who is very tall but very light, without flagging the person who is both tall and heavy. - -```{r model2, fig.cap = "The leverage method (Cook's distance) correctly distinguishes the true outlier from the model-consistent extreme observation)."} -outliers <- check_outliers(model, method = "cook") -which(outliers) -plot(outliers) -``` - -Finally, unusual observations happen naturally: extreme observations are expected even when taken from a normal distribution. While statistical models can integrate this "expectation", multivariate outlier methods might be too conservative, flagging too many observations despite belonging to the right generative process. For these reasons, we believe that model-based methods are still preferable to the MCD when using supported regression models. Additionally, if the presence of multiple outliers is a significant concern, regression methods that are more robust to outliers should be considered---like _t_ regression or quantile regression---as they render their precise identification less critical [@mcelreath2020statistical]. - -## Multiple Methods - -An alternative approach that is possible is to combine several methods, based on the assumption that different methods provide different angles of looking at the problem. By applying a variety of methods, one can hope to "triangulate" the true outliers (those consistently flagged by multiple methods) and thus attempt to minimize false positives. - -In practice, this approach computes a composite outlier score, formed of the average of the binary (0 or 1) classification results of each method. It represents the probability that each observation is classified as an outlier by at least one method. The default decision rule classifies rows with composite outlier scores superior or equal to 0.5 as outlier observations (i.e., that were classified as outliers by at least half of the methods). In *{performance}*'s `check_outliers()`, one can use this approach by including all desired methods in the corresponding argument. - -```{r multimethod, fig.cap = "Visual depiction of outliers using several different statistical outlier detection methods."} -outliers <- check_outliers(model, method = c("zscore_robust", "mcd", "cook")) -which(outliers) -``` - -Outliers (counts or per variables) for individual methods can then be obtained through attributes. For example: - -```{r} -attributes(outliers)$outlier_var$zscore_robust -``` - -An example sentence for reporting the usage of the composite method could be: - -> Based on a composite outlier score (see the 'check_outliers()' function in the 'performance' R package, [@ludecke2021performance]) obtained via the joint application of multiple outliers detection algorithms ((a) median absolute deviation (MAD)-based robust _z_ scores, [@leys2013outliers]; (b) Mahalanobis minimum covariance determinant (MCD), [@leys2019outliers]; and (c) Cook's distance, [@cook1977detection]), we excluded two participants that were classified as outliers by at least half of the methods used. - -# Handling Outliers - -The above section demonstrated how to identify outliers using the `check_outliers()` function in the *{performance}* package. But what should we do with these outliers once identified? Although it is common to automatically discard any observation that has been marked as "an outlier" as if it might infect the rest of the data with its statistical ailment, we believe that the use of SOD methods is but one step in the get-to-know-your-data pipeline; a researcher or analyst's _domain knowledge_ must be involved in the decision of how to deal with observations marked as outliers by means of SOD. Indeed, automatic tools can help detect outliers, but they are nowhere near perfect. Although they can be useful to flag suspect data, they can have misses and false alarms, and they cannot replace human eyes and proper vigilance from the researcher. If you do end up manually inspecting your data for outliers, it can be helpful to think of outliers as belonging to different types of outliers, or categories, which can help decide what to do with a given outlier. - -## Error, Interesting, and Random Outliers - -@leys2019outliers distinguish between error outliers, interesting outliers, and random outliers. _Error outliers_ are likely due to human error and should be corrected before data analysis or outright removed since they are invalid observations. _Interesting outliers_ are not due to technical error and may be of theoretical interest; it might thus be relevant to investigate them further even though they should be removed from the current analysis of interest. _Random outliers_ are assumed to be due to chance alone and to belong to the correct distribution and, therefore, should be retained. - -It is recommended to _keep_ observations which are expected to be part of the distribution of interest, even if they are outliers [@leys2019outliers]. However, if it is suspected that the outliers belong to an alternative distribution, then those observations could have a large impact on the results and call into question their robustness, especially if significance is conditional on their inclusion. - -On the other hand, there are also outliers that cannot be detected by statistical tools, but should be found and removed. For example, if we are studying the effects of X on Y among teenagers and we have one observation from a 20-year-old, this observation might not be a _statistical outlier_, but it is an outlier in the _context_ of our research, and should be discarded to allow for valid inferences. - -## Winsorization - -_Removing_ outliers can in this case be a valid strategy, and ideally one would report results with and without outliers to see the extent of their impact on results. This approach however can reduce statistical power. Therefore, some propose a _recoding_ approach, namely, winsorization: bringing outliers back within acceptable limits [e.g., 3 MADs, @tukey1963less]. However, if possible, it is recommended to collect enough data so that even after removing outliers, there is still sufficient statistical power without having to resort to winsorization [@leys2019outliers]. - -The _easystats_ ecosystem makes it easy to incorporate this step into your workflow through the `winsorize()` function of *{datawizard}*, a lightweight R package to facilitate data wrangling and statistical transformations [@patil2022datawizard]. This procedure will bring back univariate outliers within the limits of 'acceptable' values, based either on the percentile, the _z_ score, or its robust alternative based on the MAD. - -```{r winsorization} -data[1501:1502, ] # See outliers rows - -# Winsorizing using the MAD -library(datawizard) -winsorized_data <- winsorize(data, method = "zscore", robust = TRUE, threshold = 3) - -# Values > +/- MAD have been winsorized -winsorized_data[1501:1502, ] -``` - -## The Importance of Transparency - -Once again, it is a critical part of a sound outlier treatment that regardless of which SOD method used, it should be reported in a reproducible manner. Ideally, the handling of outliers should be specified *a priori* with as much detail as possible, and preregistered, to limit researchers' degrees of freedom and therefore risks of false positives [@leys2019outliers]. This is especially true given that interesting outliers and random outliers are often times hard to distinguish in practice. Thus, researchers should always prioritize transparency and report all of the following information: (a) how many outliers were identified; (b) according to which method and criteria, (c) using which function of which R package (if applicable), and (d) how they were handled (excluded or winsorized, if the latter, using what threshold). If at all possible, (e) the corresponding code script along with the data should be shared on a public repository like the Open Science Framework (OSF), so that the exclusion criteria can be reproduced precisely. - -# Conclusion - -In this paper, we have showed how to investigate outliers using the `check_outliers()` function of the *{performance}* package while following current good practices. However, best practice for outlier treatment does not stop at using appropriate statistical algorithms, but entails respecting existing recommendations, such as preregistration, reproducibility, consistency, transparency, and justification. Ideally, one would additionally also report the package, function, and threshold used (linking to the full code when possible). 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-#> - Based on the following method and threshold: zscore_robust (3.291). -#> - For variables: mpg, cyl, disp, hp. -#> -#> ----------------------------------------------------------------------------- -#> -#> The following observations were considered outliers for two or more -#> variables by at least one of the selected methods: -#> -#> Row car n_Zscore_robust -#> 1 33 33 2 -#> 2 34 34 2 -#> -#> ----------------------------------------------------------------------------- -#> Outliers per variable (zscore_robust): -#> -#> $mpg -#> Row car Distance_Zscore_robust -#> 33 33 33 3.709699 -#> 34 34 34 5.848328 -#> -#> $cyl -#> Row car Distance_Zscore_robust -#> 33 33 33 12.14083 -#> 34 34 34 16.52502 -\end{verbatim} - -The row numbers of the detected outliers can be obtained by using -\texttt{which()} on the output object, which can be used for exclusions -for example: - -\begin{Shaded} -\begin{Highlighting}[] -\FunctionTok{which}\NormalTok{(outliers)} -\end{Highlighting} -\end{Shaded} - -\begin{verbatim} -#> [1] 33 34 -\end{verbatim} - -\begin{Shaded} -\begin{Highlighting}[] -\NormalTok{data\_clean }\OtherTok{\textless{}{-}}\NormalTok{ data[}\SpecialCharTok{{-}}\FunctionTok{which}\NormalTok{(outliers), ]} -\end{Highlighting} -\end{Shaded} - -All \texttt{check\_outliers()} output objects possess a \texttt{plot()} -method, meaning it is also possible to visualize the outliers: - -\begin{Shaded} -\begin{Highlighting}[] -\FunctionTok{library}\NormalTok{(see)} - -\FunctionTok{plot}\NormalTok{(outliers)} -\end{Highlighting} -\end{Shaded} - -\begin{figure} -\includegraphics[width=1\linewidth]{paper_files/figure-latex/univariate-1} \caption{Visual depiction of outliers using the robust z-score method.}\label{fig:univariate} -\end{figure} - -Other univariate methods are available, such as using the interquartile -range (IQR), or based on different intervals, such as the Highest -Density Interval (HDI) or the Bias Corrected and Accelerated Interval -(BCI). These methods are documented and described in the function's -\href{https://easystats.github.io/performance/reference/check_outliers.html}{help -page}. - -\hypertarget{multivariate-outliers}{% -\subsection{Multivariate Outliers}\label{multivariate-outliers}} - -Univariate outliers can be useful when the focus is on a particular -variable, for instance the reaction time, as extreme values might be -indicative of inattention or non-task-related behavior\footnote{ Note - that they might not be the optimal way of treating reaction time - outliers \citep{ratcliff1993methods, van1995statistical}}. - -However, in many scenarios, variables of a data set are not independent, -and an abnormal observation will impact multiple dimensions. For -instance, a participant giving random answers to a questionnaire. In -this case, computing the \emph{z} score for each of the questions might -not lead to satisfactory results. Instead, one might want to look at -these variables together. - -One common approach for this is to compute multivariate distance metrics -such as the Mahalanobis distance. Although the Mahalanobis distance is -very popular, just like the regular \emph{z} scores method, it is not -robust and is heavily influenced by the outliers themselves. Therefore, -for multivariate outliers, it is recommended to use the Minimum -Covariance Determinant, a robust version of the Mahalanobis distance -\citep[MCD,][]{leys2018outliers, leys2019outliers}. - -In \emph{\{performance\}}'s \texttt{check\_outliers()}, one can use this -approach with \texttt{method\ =\ "mcd"}.\footnote{Our default threshold - for the MCD method is defined by - \texttt{stats::qchisq(p\ =\ 1\ -\ 0.001,\ df\ =\ ncol(x))}, which - again is an approximation of the critical value for \emph{p} - \textless{} .001 consistent with the thresholds of our other methods.} - -\begin{Shaded} -\begin{Highlighting}[] -\NormalTok{outliers }\OtherTok{\textless{}{-}} \FunctionTok{check\_outliers}\NormalTok{(data, }\AttributeTok{method =} \StringTok{"mcd"}\NormalTok{)} -\NormalTok{outliers} -\end{Highlighting} -\end{Shaded} - -\begin{verbatim} -#> 9 outliers detected: cases 7, 15, 16, 17, 24, 29, 31, 33, 34. -#> - Based on the following method and threshold: mcd (20). -#> - For variables: mpg, cyl, disp, hp. -\end{verbatim} - -\begin{Shaded} -\begin{Highlighting}[] -\FunctionTok{plot}\NormalTok{(outliers)} -\end{Highlighting} -\end{Shaded} - -\begin{figure} -\includegraphics[width=1\linewidth]{paper_files/figure-latex/multivariate-1} \caption{Visual depiction of outliers using the Minimum Covariance Determinant (MCD) method, a robust version of the Mahalanobis distance.}\label{fig:multivariate} -\end{figure} - -Other multivariate methods are available, such as another type of robust -Mahalanobis distance that in this case relies on an orthogonalized -Gnanadesikan-Kettenring pairwise estimator -\citep{gnanadesikan1972robust}. These methods are documented and -described in the function's -\href{https://easystats.github.io/performance/reference/check_outliers.html}{help -page}. - -\hypertarget{model-based-outliers}{% -\subsection{Model-Based Outliers}\label{model-based-outliers}} - -Working with regression models creates the possibility of using -model-based SOD methods. These methods rely on the concept of -\emph{leverage}, that is, how much influence a given observation can -have on the model estimates. If few observations have a relatively -strong leverage/influence on the model, one can suspect that the model's -estimates are biased by these observations, in which case flagging them -as outliers could prove helpful (see next section, ``Handling -Outliers''). - -In \{performance\}, two such model-based SOD methods are currently -available: Cook's distance, for regular regression models, and Pareto, -for Bayesian models. As such, \texttt{check\_outliers()} can be applied -directly on regression model objects, by simply specifying -\texttt{method\ =\ "cook"} (or \texttt{method\ =\ "pareto"} for Bayesian -models).\footnote{Our default threshold for the Cook method is defined - by \texttt{stats::qf(0.5,\ ncol(x),\ nrow(x)\ -\ ncol(x))}, which - again is an approximation of the critical value for \emph{p} - \textless{} .001 consistent with the thresholds of our other methods.} - -\begin{Shaded} -\begin{Highlighting}[] -\NormalTok{model }\OtherTok{\textless{}{-}} \FunctionTok{lm}\NormalTok{(disp }\SpecialCharTok{\textasciitilde{}}\NormalTok{ mpg }\SpecialCharTok{*}\NormalTok{ disp, }\AttributeTok{data =}\NormalTok{ data)} -\NormalTok{outliers }\OtherTok{\textless{}{-}} \FunctionTok{check\_outliers}\NormalTok{(model, }\AttributeTok{method =} \StringTok{"cook"}\NormalTok{)} -\NormalTok{outliers} -\end{Highlighting} -\end{Shaded} - -\begin{verbatim} -#> 1 outlier detected: case 34. -#> - Based on the following method and threshold: cook (0.708). -#> - For variable: (Whole model). -\end{verbatim} - -\begin{Shaded} -\begin{Highlighting}[] -\FunctionTok{plot}\NormalTok{(outliers)} -\end{Highlighting} -\end{Shaded} - -\begin{figure} -\includegraphics[width=1\linewidth]{paper_files/figure-latex/model-1} \caption{Visual depiction of outliers based on Cook's distance (leverage and standardized residuals).}\label{fig:model} -\end{figure} - -Table 1 below summarizes which methods to use in which cases, and with -what threshold. - -\begin{longtable}[]{@{} - >{\raggedright\arraybackslash}p{(\columnwidth - 4\tabcolsep) * \real{0.3506}} - >{\raggedright\arraybackslash}p{(\columnwidth - 4\tabcolsep) * \real{0.3161}} - >{\raggedright\arraybackslash}p{(\columnwidth - 4\tabcolsep) * \real{0.3333}}@{}} -\caption{Summary of Statistical Outlier Detection Methods -Recommendations.}\tabularnewline -\toprule() -\begin{minipage}[b]{\linewidth}\raggedright -Statistical Test -\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedright -Diagnosis Method -\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedright -Recommended Threshold -\end{minipage} \\ -\midrule() -\endfirsthead -\toprule() -\begin{minipage}[b]{\linewidth}\raggedright -Statistical Test -\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedright -Diagnosis Method -\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedright -Recommended Threshold -\end{minipage} \\ -\midrule() -\endhead -Supported regression model & \textbf{Model-based}: Cook (or Pareto for -Bayesian models) & \texttt{qf(0.5,\ ncol(x),\ nrow(x)\ -\ ncol(x))} (or -0.7 for Pareto) \\ -Structural Equation Modeling (or other unsupported model) & -\textbf{Multivariate}: Minimum Covariance Determinant (MCD) & -\texttt{qchisq(p\ =\ 1\ -\ 0.001,\ df\ =\ ncol(x))} \\ -Simple test with few variables (\emph{t} test, correlation, etc.) & -\textbf{Univariate}: robust \emph{z} scores (MAD) & -\texttt{qnorm(p\ =\ 1\ -\ 0.001\ /\ 2)}, \textasciitilde{} 3.29 \\ -\bottomrule() -\end{longtable} - -\hypertarget{cooks-distance-vs.-mcd}{% -\subsubsection{Cook's Distance vs.~MCD}\label{cooks-distance-vs.-mcd}} - -\citet{leys2018outliers} report a preference for the MCD method over -Cook's distance. This is because Cook's distance removes one observation -at a time and checks its corresponding influence on the model each time -\citep{cook1977detection}, and flags any observation that has a large -influence. In the view of these authors, when there are several -outliers, the process of removing a single outlier at a time is -problematic as the model remains ``contaminated'' or influenced by other -possible outliers in the model, rendering this method suboptimal in the -presence of multiple outliers. - -However, distribution-based approaches are not a silver bullet either, -and there are cases where the usage of methods agnostic to theoretical -and statistical models of interest might be problematic. For example, a -very tall person would be expected to also be much heavier than average, -but that would still fit with the expected association between height -and weight (i.e., it would be in line with a model such as -\texttt{weight\ \textasciitilde{}\ height}). In contrast, using -multivariate outlier detection methods there may flag this person as -being an outlier---being unusual on two variables, height and -weight---even though the pattern fits perfectly with our predictions. - -In the example below, we plot the raw data and see two possible -outliers. The first one falls along the regression line, and is -therefore ``in line'' with our hypothesis. The second one clearly -diverges from the regression line, and therefore we can conclude that -this outlier may have a disproportionate influence on our model. - -\begin{Shaded} -\begin{Highlighting}[] -\NormalTok{data }\OtherTok{\textless{}{-}}\NormalTok{ women[}\FunctionTok{rep}\NormalTok{(}\FunctionTok{seq\_len}\NormalTok{(}\FunctionTok{nrow}\NormalTok{(women)), }\AttributeTok{each =} \DecValTok{100}\NormalTok{), ]} -\NormalTok{data }\OtherTok{\textless{}{-}} \FunctionTok{rbind}\NormalTok{(data, }\FunctionTok{c}\NormalTok{(}\DecValTok{100}\NormalTok{, }\DecValTok{258}\NormalTok{), }\FunctionTok{c}\NormalTok{(}\DecValTok{100}\NormalTok{, }\DecValTok{200}\NormalTok{))} -\NormalTok{model }\OtherTok{\textless{}{-}} \FunctionTok{lm}\NormalTok{(weight }\SpecialCharTok{\textasciitilde{}}\NormalTok{ height, data)} -\NormalTok{rempsyc}\SpecialCharTok{::}\FunctionTok{nice\_scatter}\NormalTok{(data, }\StringTok{"height"}\NormalTok{, }\StringTok{"weight"}\NormalTok{)} -\end{Highlighting} -\end{Shaded} - -\begin{figure} -\includegraphics[width=1\linewidth]{paper_files/figure-latex/scatter-1} \caption{Scatter plot of height and weight, with two extreme observations: one model-consistent (top-right) and the other, model-inconsistent (i.e., an outlier; bottom-right).}\label{fig:scatter} -\end{figure} - -Using either the \emph{z}-score or MCD methods, our model-consistent -observation will be incorrectly flagged as an outlier or influential -observation. - -\begin{Shaded} -\begin{Highlighting}[] -\NormalTok{outliers }\OtherTok{\textless{}{-}} \FunctionTok{check\_outliers}\NormalTok{(model, }\AttributeTok{method =} \FunctionTok{c}\NormalTok{(}\StringTok{"zscore\_robust"}\NormalTok{, }\StringTok{"mcd"}\NormalTok{))} -\FunctionTok{which}\NormalTok{(outliers)} -\end{Highlighting} -\end{Shaded} - -\begin{verbatim} -#> [1] 1501 1502 -\end{verbatim} - -In contrast, the model-based detection method displays the desired -behaviour: it correctly flags the person who is very tall but very -light, without flagging the person who is both tall and heavy. - -\begin{Shaded} -\begin{Highlighting}[] -\NormalTok{outliers }\OtherTok{\textless{}{-}} \FunctionTok{check\_outliers}\NormalTok{(model, }\AttributeTok{method =} \StringTok{"cook"}\NormalTok{)} -\FunctionTok{which}\NormalTok{(outliers)} -\end{Highlighting} -\end{Shaded} - -\begin{verbatim} -#> [1] 1502 -\end{verbatim} - -\begin{Shaded} -\begin{Highlighting}[] -\FunctionTok{plot}\NormalTok{(outliers)} -\end{Highlighting} -\end{Shaded} - -\begin{figure} -\includegraphics[width=1\linewidth]{paper_files/figure-latex/model2-1} \caption{The leverage method (Cook's distance) correctly distinguishes the true outlier from the model-consistent extreme observation).}\label{fig:model2} -\end{figure} - -Finally, unusual observations happen naturally: extreme observations are -expected even when taken from a normal distribution. While statistical -models can integrate this ``expectation'', multivariate outlier methods -might be too conservative, flagging too many observations despite -belonging to the right generative process. For these reasons, we believe -that model-based methods are still preferable to the MCD when using -supported regression models. Additionally, if the presence of multiple -outliers is a significant concern, regression methods that are more -robust to outliers should be considered---like \emph{t} regression or -quantile regression---as they render their precise identification less -critical \citep{mcelreath2020statistical}. - -\hypertarget{multiple-methods}{% -\subsection{Multiple Methods}\label{multiple-methods}} - -An alternative approach that is possible is to combine several methods, -based on the assumption that different methods provide different angles -of looking at the problem. By applying a variety of methods, one can -hope to ``triangulate'' the true outliers (those consistently flagged by -multiple methods) and thus attempt to minimize false positives. - -In practice, this approach computes a composite outlier score, formed of -the average of the binary (0 or 1) classification results of each -method. It represents the probability that each observation is -classified as an outlier by at least one method. The default decision -rule classifies rows with composite outlier scores superior or equal to -0.5 as outlier observations (i.e., that were classified as outliers by -at least half of the methods). In \emph{\{performance\}}'s -\texttt{check\_outliers()}, one can use this approach by including all -desired methods in the corresponding argument. - -\begin{Shaded} -\begin{Highlighting}[] -\NormalTok{outliers }\OtherTok{\textless{}{-}} \FunctionTok{check\_outliers}\NormalTok{(model, }\AttributeTok{method =} \FunctionTok{c}\NormalTok{(}\StringTok{"zscore\_robust"}\NormalTok{, }\StringTok{"mcd"}\NormalTok{, }\StringTok{"cook"}\NormalTok{))} -\FunctionTok{which}\NormalTok{(outliers)} -\end{Highlighting} -\end{Shaded} - -\begin{verbatim} -#> [1] 1501 1502 -\end{verbatim} - -Outliers (counts or per variables) for individual methods can then be -obtained through attributes. For example: - -\begin{Shaded} -\begin{Highlighting}[] -\FunctionTok{attributes}\NormalTok{(outliers)}\SpecialCharTok{$}\NormalTok{outlier\_var}\SpecialCharTok{$}\NormalTok{zscore\_robust} -\end{Highlighting} -\end{Shaded} - -\begin{verbatim} -#> $weight -#> Row Distance_Zscore_robust -#> 1501 1501 6.913530 -#> 1502 1502 3.653492 -#> -#> $height -#> Row Distance_Zscore_robust -#> 1501 1501 5.901794 -#> 1502 1502 5.901794 -\end{verbatim} - -An example sentence for reporting the usage of the composite method -could be: - -\begin{quote} -Based on a composite outlier score (see the `check\_outliers()' function -in the `performance' R package, \citep{ludecke2021performance}) obtained -via the joint application of multiple outliers detection algorithms ((a) -median absolute deviation (MAD)-based robust \emph{z} scores, -\citep{leys2013outliers}; (b) Mahalanobis minimum covariance determinant -(MCD), \citep{leys2019outliers}; and (c) Cook's distance, -\citep{cook1977detection}), we excluded two participants that were -classified as outliers by at least half of the methods used. -\end{quote} - -\hypertarget{handling-outliers}{% -\section{Handling Outliers}\label{handling-outliers}} - -The above section demonstrated how to identify outliers using the -\texttt{check\_outliers()} function in the \emph{\{performance\}} -package. But what should we do with these outliers once identified? -Although it is common to automatically discard any observation that has -been marked as ``an outlier'' as if it might infect the rest of the data -with its statistical ailment, we believe that the use of SOD methods is -but one step in the get-to-know-your-data pipeline; a researcher or -analyst's \emph{domain knowledge} must be involved in the decision of -how to deal with observations marked as outliers by means of SOD. -Indeed, automatic tools can help detect outliers, but they are nowhere -near perfect. Although they can be useful to flag suspect data, they can -have misses and false alarms, and they cannot replace human eyes and -proper vigilance from the researcher. If you do end up manually -inspecting your data for outliers, it can be helpful to think of -outliers as belonging to different types of outliers, or categories, -which can help decide what to do with a given outlier. - -\hypertarget{error-interesting-and-random-outliers}{% -\subsection{Error, Interesting, and Random -Outliers}\label{error-interesting-and-random-outliers}} - -\citet{leys2019outliers} distinguish between error outliers, interesting -outliers, and random outliers. \emph{Error outliers} are likely due to -human error and should be corrected before data analysis or outright -removed since they are invalid observations. \emph{Interesting outliers} -are not due to technical error and may be of theoretical interest; it -might thus be relevant to investigate them further even though they -should be removed from the current analysis of interest. \emph{Random -outliers} are assumed to be due to chance alone and to belong to the -correct distribution and, therefore, should be retained. - -It is recommended to \emph{keep} observations which are expected to be -part of the distribution of interest, even if they are outliers -\citep{leys2019outliers}. However, if it is suspected that the outliers -belong to an alternative distribution, then those observations could -have a large impact on the results and call into question their -robustness, especially if significance is conditional on their -inclusion. - -On the other hand, there are also outliers that cannot be detected by -statistical tools, but should be found and removed. For example, if we -are studying the effects of X on Y among teenagers and we have one -observation from a 20-year-old, this observation might not be a -\emph{statistical outlier}, but it is an outlier in the \emph{context} -of our research, and should be discarded to allow for valid inferences. - -\hypertarget{winsorization}{% -\subsection{Winsorization}\label{winsorization}} - -\emph{Removing} outliers can in this case be a valid strategy, and -ideally one would report results with and without outliers to see the -extent of their impact on results. This approach however can reduce -statistical power. Therefore, some propose a \emph{recoding} approach, -namely, winsorization: bringing outliers back within acceptable limits -\citep[e.g., 3 MADs,][]{tukey1963less}. However, if possible, it is -recommended to collect enough data so that even after removing outliers, -there is still sufficient statistical power without having to resort to -winsorization \citep{leys2019outliers}. - -The \emph{easystats} ecosystem makes it easy to incorporate this step -into your workflow through the \texttt{winsorize()} function of -\emph{\{datawizard\}}, a lightweight R package to facilitate data -wrangling and statistical transformations \citep{patil2022datawizard}. -This procedure will bring back univariate outliers within the limits of -`acceptable' values, based either on the percentile, the \emph{z} score, -or its robust alternative based on the MAD. - -\begin{Shaded} -\begin{Highlighting}[] -\NormalTok{data[}\DecValTok{1501}\SpecialCharTok{:}\DecValTok{1502}\NormalTok{, ] }\CommentTok{\# See outliers rows} -\end{Highlighting} -\end{Shaded} - -\begin{verbatim} -#> height weight -#> 1501 100 258 -#> 1502 100 200 -\end{verbatim} - -\begin{Shaded} -\begin{Highlighting}[] -\CommentTok{\# Winsorizing using the MAD} -\FunctionTok{library}\NormalTok{(datawizard)} -\NormalTok{winsorized\_data }\OtherTok{\textless{}{-}} \FunctionTok{winsorize}\NormalTok{(data, }\AttributeTok{method =} \StringTok{"zscore"}\NormalTok{, }\AttributeTok{robust =} \ConstantTok{TRUE}\NormalTok{, }\AttributeTok{threshold =} \DecValTok{3}\NormalTok{)} - -\CommentTok{\# Values \textgreater{} +/{-} MAD have been winsorized} -\NormalTok{winsorized\_data[}\DecValTok{1501}\SpecialCharTok{:}\DecValTok{1502}\NormalTok{, ]} -\end{Highlighting} -\end{Shaded} - -\begin{verbatim} -#> height weight -#> 1501 82.7912 188.3736 -#> 1502 82.7912 188.3736 -\end{verbatim} - -\hypertarget{the-importance-of-transparency}{% -\subsection{The Importance of -Transparency}\label{the-importance-of-transparency}} - -Once again, it is a critical part of a sound outlier treatment that -regardless of which SOD method used, it should be reported in a -reproducible manner. Ideally, the handling of outliers should be -specified \emph{a priori} with as much detail as possible, and -preregistered, to limit researchers' degrees of freedom and therefore -risks of false positives \citep{leys2019outliers}. This is especially -true given that interesting outliers and random outliers are often times -hard to distinguish in practice. Thus, researchers should always -prioritize transparency and report all of the following information: (a) -how many outliers were identified; (b) according to which method and -criteria, (c) using which function of which R package (if applicable), -and (d) how they were handled (excluded or winsorized, if the latter, -using what threshold). If at all possible, (e) the corresponding code -script along with the data should be shared on a public repository like -the Open Science Framework (OSF), so that the exclusion criteria can be -reproduced precisely. - -\hypertarget{conclusion}{% -\section{Conclusion}\label{conclusion}} - -In this paper, we have showed how to investigate outliers using the -\texttt{check\_outliers()} function of the \emph{\{performance\}} -package while following current good practices. However, best practice -for outlier treatment does not stop at using appropriate statistical -algorithms, but entails respecting existing recommendations, such as -preregistration, reproducibility, consistency, transparency, and -justification. Ideally, one would additionally also report the package, -function, and threshold used (linking to the full code when possible). -We hope that this paper and the accompanying \texttt{check\_outlier()} -function of \emph{easystats} will help researchers engage in good -research practices while providing a smooth outlier detection -experience. - -% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% %% optional -% \supplementary{The following are available online at www.mdpi.com/link, Figure S1: title, Table S1: title, Video S1: title.} -% -% % Only for the journal Methods and Protocols: -% % If you wish to submit a video article, please do so with any other supplementary material. -% % \supplementary{The following are available at www.mdpi.com/link: Figure S1: title, Table S1: title, Video S1: title. A supporting video article is available at doi: link.} - -\vspace{6pt} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\acknowledgments{\emph{\{performance\}} is part of the collaborative -\href{https://github.com/easystats/easystats}{\emph{easystats}} -ecosystem \citep{easystatspackage}. Thus, we thank all -\href{https://github.com/orgs/easystats/people}{members of easystats}, -contributors, and users alike.} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\authorcontributions{R.T. drafted the paper; all authors contributed to -both the writing of the paper and the conception of the software.} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\conflictsofinterest{The authors declare no conflict of interest.} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% optional -\abbreviations{The following abbreviations are used in this manuscript:\\ - -\noindent -\begin{tabular}{@{}ll} -SOD & Statistical outlier detection \\ -SEM & Structural equation modelling \\ -SD & Standard deviation \\ -MAD & Median absolute deviation \\ -IQR & Interquartile range \\ -HDI & Highest density interval \\ -BCI & Bias corrected and accelerated interval \\ -MCD & Minimum covariance determinant \\ -ICS & invariant coordinate selection \\ -OSF & Open Science Framework \\ -\end{tabular}} - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% Citations and References in Supplementary files are permitted provided that they also appear in the reference list here. - -%===================================== -% References, variant A: internal bibliography -%===================================== -%\reftitle{References} -%\begin{thebibliography}{999} -% Reference 1 -%\bibitem[Author1(year)]{ref-journal} -%Author1, T. The title of the cited article. {\em Journal Abbreviation} {\bf 2008}, {\em 10}, 142--149. -% Reference 2 -%\bibitem[Author2(year)]{ref-book} -%Author2, L. The title of the cited contribution. In {\em The Book Title}; Editor1, F., Editor2, A., Eds.; Publishing House: City, Country, 2007; pp. 32--58. -%\end{thebibliography} - -% The following MDPI journals use author-date citation: Arts, Econometrics, Economies, Genealogy, Humanities, IJFS, JRFM, Laws, Religions, Risks, Social Sciences. For those journals, please follow the formatting guidelines on http://www.mdpi.com/authors/references -% To cite two works by the same author: \citeauthor{ref-journal-1a} (\citeyear{ref-journal-1a}, \citeyear{ref-journal-1b}). This produces: Whittaker (1967, 1975) -% To cite two works by the same author with specific pages: \citeauthor{ref-journal-3a} (\citeyear{ref-journal-3a}, p. 328; \citeyear{ref-journal-3b}, p.475). This produces: Wong (1999, p. 328; 2000, p. 475) - -%===================================== -% References, variant B: external bibliography -%===================================== -\reftitle{References} -\externalbibliography{yes} -\bibliography{mybibfile.bib} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% optional - -%% for journal Sci -%\reviewreports{\\ -%Reviewer 1 comments and authors’ response\\ -%Reviewer 2 comments and authors’ response\\ -%Reviewer 3 comments and authors’ response -%} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - - -\end{document} diff --git a/papers/Mathematics/paper_files/figure-latex/model-1.pdf b/papers/Mathematics/paper_files/figure-latex/model-1.pdf deleted file mode 100644 index b146f331731f18d81d5eb5fc27a2895bbb0712fa..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 7822 zcmZ{pcRZY1^T0)dAR&kr!V*1LR_}@4%c{|ZC0M)4D$!dIi$w24v>=GyJCQ`MiOwPf 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steps: + - name: Checkout + uses: actions/checkout@v2 + - name: Build draft PDF + uses: openjournals/openjournals-draft-action@master + with: + journal: jose + # This should be the path to the paper within your repo. + paper-path: paper/paper.md + - name: Upload + uses: actions/upload-artifact@v1 + with: + name: paper + # This is the output path where Pandoc will write the compiled + # PDF. Note, this should be the same directory as the input + # paper.md + path: paper/paper.pdf + - name: save pdf to repo + uses: stefanzweifel/git-auto-commit-action@v4 + with: + commit_message: Saved new PDF of paper diff --git a/papers/JOSE/mybibfile.bib b/papers/JOSE/mybibfile.bib index 08b5ba5d0..56c8ae7e1 100644 --- a/papers/JOSE/mybibfile.bib +++ b/papers/JOSE/mybibfile.bib @@ -51,7 +51,7 @@ @software{easystatspackage @Article{ludecke2021performance, author = {Daniel Lüdecke and Mattan S. Ben-Shachar and Indrajeet Patil and Philip Waggoner and Dominique Makowski}, - title = {{performance}: An R package for assessment, comparison and testing of statistical models}, + title = {{performance}: An {R} package for assessment, comparison and testing of statistical models}, volume = {6}, number = {60}, journal = {Journal of Open Source Software}, From 7cb2029db1fa5a7a3b82f551ae1597efc5d65f73 Mon Sep 17 00:00:00 2001 From: rempsyc Date: Wed, 7 Jun 2023 12:32:14 -0400 Subject: [PATCH 11/34] update JOSE action --- .github/workflows/draft-pdf.yml | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/.github/workflows/draft-pdf.yml b/.github/workflows/draft-pdf.yml index 7354d2486..944e50ca8 100644 --- a/.github/workflows/draft-pdf.yml +++ b/.github/workflows/draft-pdf.yml @@ -12,7 +12,7 @@ jobs: with: journal: jose # This should be the path to the paper within your repo. - paper-path: paper/paper.md + paper-path: papers/JOSE/paper.md - name: Upload uses: actions/upload-artifact@v1 with: @@ -20,7 +20,7 @@ jobs: # This is the output path where Pandoc will write the compiled # PDF. Note, this should be the same directory as the input # paper.md - path: paper/paper.pdf + path: papers/JOSE/paper.pdf - name: save pdf to repo uses: stefanzweifel/git-auto-commit-action@v4 with: From f31286bd5bc9fdc192ddf9a650a7f9f38349ec69 Mon Sep 17 00:00:00 2001 From: rempsyc Date: Wed, 7 Jun 2023 12:47:00 -0400 Subject: [PATCH 12/34] add tags, date --- papers/JOSE/paper.Rmd | 7 +++++++ 1 file changed, 7 insertions(+) diff --git a/papers/JOSE/paper.Rmd b/papers/JOSE/paper.Rmd index 9b47e2f5c..d03862f55 100644 --- a/papers/JOSE/paper.Rmd +++ b/papers/JOSE/paper.Rmd @@ -1,5 +1,11 @@ --- title: "Check your outliers! An introduction to identifying statistical outliers in R with *easystats*" +tags: + - R + - univariate outliers + - multivariate outliers + - robust detection methods + - easystats authors: - name: Rémi Thériault orcid: 0000-0003-4315-6788 @@ -35,6 +41,7 @@ affiliations: correspondence: theriault.remi@courrier.uqam.ca. type: article status: submit +date: 7 June 2023 bibliography: mybibfile.bib simplesummary: | The *{performance}* package from the *easystats* ecosystem makes it easy to From b75c2741dd1ac6d738fa3c591f36f4315f09f056 Mon Sep 17 00:00:00 2001 From: rempsyc Date: Wed, 7 Jun 2023 13:06:24 -0400 Subject: [PATCH 13/34] remove save pdf to repo action --- .github/workflows/draft-pdf.yml | 4 ---- 1 file changed, 4 deletions(-) diff --git a/.github/workflows/draft-pdf.yml b/.github/workflows/draft-pdf.yml index 944e50ca8..890d6dd6c 100644 --- a/.github/workflows/draft-pdf.yml +++ b/.github/workflows/draft-pdf.yml @@ -21,7 +21,3 @@ jobs: # PDF. Note, this should be the same directory as the input # paper.md path: papers/JOSE/paper.pdf - - name: save pdf to repo - uses: stefanzweifel/git-auto-commit-action@v4 - with: - commit_message: Saved new PDF of paper From 194d53d901ea8241d7fc915d3155dc9bee804ea5 Mon Sep 17 00:00:00 2001 From: rempsyc Date: Wed, 7 Jun 2023 15:44:38 -0400 Subject: [PATCH 14/34] knit paper --- papers/JOSE/paper.log | 856 ++++++------------ papers/JOSE/paper.md | 7 + papers/JOSE/paper.pdf | Bin 234058 -> 238373 bytes .../JOSE/paper_files/figure-latex/model-1.pdf | Bin 5092 -> 8475 bytes .../paper_files/figure-latex/model2-1.pdf | Bin 8533 -> 9186 bytes .../figure-latex/multivariate_implicit-1.pdf | Bin 5104 -> 5785 bytes .../paper_files/figure-latex/scatter-1.pdf | Bin 7724 -> 8383 bytes .../figure-latex/univariate_implicit-1.pdf | Bin 5117 -> 5796 bytes 8 files changed, 305 insertions(+), 558 deletions(-) diff --git a/papers/JOSE/paper.log b/papers/JOSE/paper.log index 02addf851..f8e679e1c 100644 --- a/papers/JOSE/paper.log +++ b/papers/JOSE/paper.log @@ -1,14 +1,13 @@ -This is XeTeX, Version 3.141592653-2.6-0.999994 (MiKTeX 23.1) (preloaded format=xelatex 2023.2.25) 13 MAY 2023 16:49 +This is XeTeX, Version 3.141592653-2.6-0.999995 (TeX Live 2023) (preloaded format=xelatex 2023.5.8) 7 JUN 2023 15:43 entering extended mode restricted \write18 enabled. %&-line parsing enabled. -**./paper.tex -(paper.tex +**paper.tex +(./paper.tex LaTeX2e <2022-11-01> patch level 1 -L3 programming layer <2023-02-02> (C:\Users\there\AppData\Local\Programs\MiKTeX -\tex/latex/base\article.cls +L3 programming layer <2023-05-05> (c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/base/article.cls Document Class: article 2022/07/02 v1.4n Standard LaTeX document class -(C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/base\size10.clo +(c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/base/size10.clo File: size10.clo 2022/07/02 v1.4n Standard LaTeX file (size option) ) \c@part=\count181 @@ -22,38 +21,34 @@ File: size10.clo 2022/07/02 v1.4n Standard LaTeX file (size option) \abovecaptionskip=\skip48 \belowcaptionskip=\skip49 \bibindent=\dimen140 -) -(C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/marginnote\marginnote.s -ty +) (c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/marginnote/marginnote.sty Package: marginnote 2018/08/09 v1.4b non floating margin notes for LaTeX \c@mn@abspage=\count189 -) (C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/graphics\graphicx.sty +) (c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/graphics/graphicx.sty Package: graphicx 2021/09/16 v1.2d Enhanced LaTeX Graphics (DPC,SPQR) -(C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/graphics\keyval.sty +(c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/graphics/keyval.sty Package: keyval 2022/05/29 v1.15 key=value parser (DPC) \KV@toks@=\toks16 -) (C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/graphics\graphics.sty +) (c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/graphics/graphics.sty Package: graphics 2022/03/10 v1.4e Standard LaTeX Graphics (DPC,SPQR) -(C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/graphics\trig.sty +(c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/graphics/trig.sty Package: trig 2021/08/11 v1.11 sin cos tan (DPC) -) -(C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/graphics-cfg\graphics.c -fg +) (c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/graphics-cfg/graphics.cfg File: graphics.cfg 2016/06/04 v1.11 sample graphics configuration ) Package graphics Info: Driver file: xetex.def on input line 107. -(C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/graphics-def\xetex.def +(c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/graphics-def/xetex.def File: xetex.def 2022/09/22 v5.0n Graphics/color driver for xetex )) \Gin@req@height=\dimen141 \Gin@req@width=\dimen142 -) (C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/xcolor\xcolor.sty +) (c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/xcolor/xcolor.sty Package: xcolor 2022/06/12 v2.14 LaTeX color extensions (UK) -(C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/graphics-cfg\color.cfg +(c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/graphics-cfg/color.cfg File: color.cfg 2016/01/02 v1.6 sample color configuration ) Package xcolor Info: Driver file: xetex.def on input line 227. -(C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/graphics\mathcolor.ltx) +(c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/graphics/mathcolor.ltx) Package xcolor Info: Model `cmy' substituted by `cmy0' on input line 1353. 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[8] -File: C:/Users/there/AppData/Local/R/win-library/4.3/rticles/rmarkdown/template -s/joss/resources/JOSE-logo.png Graphic file (type bmp) - +File: D:/Rpackages/rticles/rmarkdown/templates/joss/resources/JOSE-logo.png Graphic file (type bmp) + Package fancyhdr Warning: \headheight is too small (62.59596pt): (fancyhdr) Make it at least 64.31554pt, for example: (fancyhdr) \setlength{\headheight}{64.31554pt}. (fancyhdr) You might also make \topmargin smaller to compensate: - (fancyhdr) \addtolength{\topmargin}{-1.71957pt}. [9] -File: C:/Users/there/AppData/Local/R/win-library/4.3/rticles/rmarkdown/template -s/joss/resources/JOSE-logo.png Graphic file (type bmp) - +File: D:/Rpackages/rticles/rmarkdown/templates/joss/resources/JOSE-logo.png Graphic file (type bmp) + Package fancyhdr Warning: \headheight is too small (62.59596pt): (fancyhdr) Make it at least 64.31554pt, for example: (fancyhdr) \setlength{\headheight}{64.31554pt}. (fancyhdr) You might also make \topmargin smaller to compensate: - (fancyhdr) \addtolength{\topmargin}{-1.71957pt}. [10] Package hyperref Warning: Difference (2) between bookmark levels is greater -(hyperref) than one, level fixed on input line 971. +(hyperref) than one, level fixed on input line 973. -File: C:/Users/there/AppData/Local/R/win-library/4.3/rticles/rmarkdown/template -s/joss/resources/JOSE-logo.png Graphic file (type bmp) - +File: D:/Rpackages/rticles/rmarkdown/templates/joss/resources/JOSE-logo.png Graphic file (type bmp) + Package fancyhdr Warning: \headheight is too small (62.59596pt): (fancyhdr) Make it at least 64.31554pt, for example: (fancyhdr) \setlength{\headheight}{64.31554pt}. (fancyhdr) You might also make \topmargin smaller to compensate: - (fancyhdr) \addtolength{\topmargin}{-1.71957pt}. [11] -Underfull \hbox (badness 1584) in paragraph at lines 1059--1065 -[]\TU/lmr/m/n/10 Simmons, J. P., Nelson, L. D., & Simonsohn, U. (2011). False-p -ositive psy- +Underfull \hbox (badness 1584) in paragraph at lines 1061--1067 +[]\TU/lmr/m/n/10 Simmons, J. P., Nelson, L. D., & Simonsohn, U. (2011). False-positive psy- [] -Underfull \hbox (badness 3049) in paragraph at lines 1059--1065 -\TU/lmr/m/n/10 chology: Undisclosed flexibility in data collection and analysis - allows pre- +Underfull \hbox (badness 3049) in paragraph at lines 1061--1067 +\TU/lmr/m/n/10 chology: Undisclosed flexibility in data collection and analysis allows pre- [] -Underfull \hbox (badness 3735) in paragraph at lines 1059--1065 -\TU/lmr/m/n/10 senting anything as significant. \TU/lmr/m/it/10 Psychological S -cience\TU/lmr/m/n/10 , \TU/lmr/m/it/10 22\TU/lmr/m/n/10 (11), 1359–1366. +Underfull \hbox (badness 3735) in paragraph at lines 1061--1067 +\TU/lmr/m/n/10 senting anything as significant. \TU/lmr/m/it/10 Psychological Science\TU/lmr/m/n/10 , \TU/lmr/m/it/10 22\TU/lmr/m/n/10 (11), 1359–1366. [] -File: C:/Users/there/AppData/Local/R/win-library/4.3/rticles/rmarkdown/template -s/joss/resources/JOSE-logo.png Graphic file (type bmp) - +File: D:/Rpackages/rticles/rmarkdown/templates/joss/resources/JOSE-logo.png Graphic file (type bmp) + Package fancyhdr Warning: \headheight is too small (62.59596pt): (fancyhdr) Make it at least 64.31554pt, for example: (fancyhdr) \setlength{\headheight}{64.31554pt}. (fancyhdr) You might also make \topmargin smaller to compensate: - (fancyhdr) \addtolength{\topmargin}{-1.71957pt}. -[12] (paper.aux) +[12] (./paper.aux) Package rerunfilecheck Info: File `paper.out' has not changed. (rerunfilecheck) Checksum: 8CE4AC14FC5D0DAC991EC18B63626103;2643. Package logreq Info: Writing requests to 'paper.run.xml'. @@ -1468,12 +1208,12 @@ Package logreq Info: Writing requests to 'paper.run.xml'. ) Here is how much of TeX's memory you used: - 37039 strings out of 411511 - 748993 string characters out of 5819115 - 1871001 words of memory out of 5000000 - 56702 multiletter control sequences out of 15000+600000 + 37207 strings out of 478705 + 767981 string characters out of 5847479 + 1871873 words of memory out of 5000000 + 56711 multiletter control sequences out of 15000+600000 519215 words of font info for 87 fonts, out of 8000000 for 9000 - 1348 hyphenation exceptions out of 8191 - 84i,12n,81p,1196b,850s stack positions out of 10000i,1000n,20000p,200000b,200000s + 14 hyphenation exceptions out of 8191 + 84i,13n,81p,1194b,848s stack positions out of 10000i,1000n,20000p,200000b,200000s Output written on paper.pdf (12 pages). diff --git a/papers/JOSE/paper.md b/papers/JOSE/paper.md index dafb1d9a5..8e488355c 100644 --- a/papers/JOSE/paper.md +++ b/papers/JOSE/paper.md @@ -1,5 +1,11 @@ --- title: "Check your outliers! 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Bin 8383 -> 8383 bytes .../figure-latex/univariate_implicit-1.pdf | Bin 5796 -> 5796 bytes 9 files changed, 5 insertions(+), 5 deletions(-) diff --git a/papers/JOSE/paper.Rmd b/papers/JOSE/paper.Rmd index d03862f55..521db2b4a 100644 --- a/papers/JOSE/paper.Rmd +++ b/papers/JOSE/paper.Rmd @@ -9,7 +9,7 @@ tags: authors: - name: Rémi Thériault orcid: 0000-0003-4315-6788 - affiliation: 1,* + affiliation: 1 - name: Mattan S. Ben-Shachar orcid: 0000-0002-4287-4801 affiliation: 2 @@ -31,7 +31,7 @@ affiliations: - index: 2 name: Independent Researcher - index: 3 - name: Center for Humans and Machines, Max Planck Institute for Human Development, Berlin, Germany + name: Center for Humans and Machines, Max Planck Institute for Human Development, Berlin, Germany - index: 4 name: Institute of Medical Sociology, University Medical Center Hamburg-Eppendorf, Germany - index: 5 diff --git a/papers/JOSE/paper.log b/papers/JOSE/paper.log index f8e679e1c..8d29a53ad 100644 --- a/papers/JOSE/paper.log +++ b/papers/JOSE/paper.log @@ -1,4 +1,4 @@ -This is XeTeX, Version 3.141592653-2.6-0.999995 (TeX Live 2023) (preloaded format=xelatex 2023.5.8) 7 JUN 2023 15:43 +This is XeTeX, Version 3.141592653-2.6-0.999995 (TeX Live 2023) (preloaded format=xelatex 2023.5.8) 7 JUN 2023 15:55 entering extended mode restricted \write18 enabled. %&-line parsing enabled. diff --git a/papers/JOSE/paper.md b/papers/JOSE/paper.md index 8e488355c..bd27c3e42 100644 --- a/papers/JOSE/paper.md +++ b/papers/JOSE/paper.md @@ -9,7 +9,7 @@ tags: authors: - name: Rémi Thériault orcid: 0000-0003-4315-6788 - affiliation: 1,* + affiliation: 1 - name: Mattan S. 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papers/JOSE/paper.Rmd | 4 +- papers/JOSE/{mybibfile.bib => paper.bib} | 0 papers/JOSE/paper.log | 69 +++++++++--------- papers/JOSE/paper.md | 4 +- papers/JOSE/paper.pdf | Bin 238220 -> 241957 bytes .../JOSE/paper_files/figure-latex/model-1.pdf | Bin 8474 -> 8479 bytes .../paper_files/figure-latex/model2-1.pdf | Bin 9192 -> 9191 bytes .../figure-latex/multivariate_implicit-1.pdf | Bin 5785 -> 5785 bytes .../paper_files/figure-latex/scatter-1.pdf | Bin 8383 -> 8383 bytes .../figure-latex/univariate_implicit-1.pdf | Bin 5796 -> 5796 bytes 10 files changed, 40 insertions(+), 37 deletions(-) rename papers/JOSE/{mybibfile.bib => paper.bib} (100%) diff --git a/papers/JOSE/paper.Rmd b/papers/JOSE/paper.Rmd index 521db2b4a..3214bde37 100644 --- a/papers/JOSE/paper.Rmd +++ b/papers/JOSE/paper.Rmd @@ -42,7 +42,7 @@ correspondence: theriault.remi@courrier.uqam.ca. type: article status: submit date: 7 June 2023 -bibliography: mybibfile.bib +bibliography: paper.bib simplesummary: | The *{performance}* package from the *easystats* ecosystem makes it easy to diagnose outliers in R and according to current best practices thanks to the @@ -116,7 +116,7 @@ library(see) library(datawizard) ``` -# Introduction +# Statement of Need Real-life data often contain observations that can be considered *abnormal* when compared to the main population. The cause of it---be it because they belong to a different distribution (originating from a different generative process) or simply being extreme cases, statistically rare but not impossible---can be hard to assess, and the boundaries of "abnormal" difficult to define. diff --git a/papers/JOSE/mybibfile.bib b/papers/JOSE/paper.bib similarity index 100% rename from papers/JOSE/mybibfile.bib rename to papers/JOSE/paper.bib diff --git a/papers/JOSE/paper.log b/papers/JOSE/paper.log index 8d29a53ad..d1524398a 100644 --- a/papers/JOSE/paper.log +++ b/papers/JOSE/paper.log @@ -1,11 +1,11 @@ -This is XeTeX, Version 3.141592653-2.6-0.999995 (TeX Live 2023) (preloaded format=xelatex 2023.5.8) 7 JUN 2023 15:55 +This is XeTeX, Version 3.141592653-2.6-0.999995 (TeX Live 2023) (preloaded format=xelatex 2023.6.8) 16 JUN 2023 15:11 entering extended mode restricted \write18 enabled. %&-line parsing enabled. **paper.tex (./paper.tex LaTeX2e <2022-11-01> patch level 1 -L3 programming layer <2023-05-05> (c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/base/article.cls +L3 programming layer <2023-06-05> (c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/base/article.cls Document Class: article 2022/07/02 v1.4n Standard LaTeX document class (c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/base/size10.clo File: size10.clo 2022/07/02 v1.4n Standard LaTeX file (size option) @@ -272,7 +272,7 @@ File: pgfmodulematrix.code.tex 2023-01-15 v3.1.10 (3.1.10) (c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarytopaths.code.tex File: tikzlibrarytopaths.code.tex 2023-01-15 v3.1.10 (3.1.10) ))) (c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/hyperref/hyperref.sty -Package: hyperref 2023-04-22 v7.00x Hypertext links for LaTeX +Package: hyperref 2023-05-16 v7.00y Hypertext links for LaTeX (c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/generic/ltxcmds/ltxcmds.sty Package: ltxcmds 2020-05-10 v1.25 LaTeX kernel commands for general use (HO) ) (c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/generic/iftex/iftex.sty @@ -298,7 +298,7 @@ Package: letltxmacro 2019/12/03 v1.6 Let assignment for LaTeX macros (HO) ) (c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/auxhook/auxhook.sty Package: auxhook 2019-12-17 v1.6 Hooks for auxiliary files (HO) ) (c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/hyperref/nameref.sty -Package: nameref 2022-05-17 v2.50 Cross-referencing by name of section +Package: nameref 2023-05-16 v2.51 Cross-referencing by name of section (c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/refcount/refcount.sty Package: refcount 2019/12/15 v3.6 Data extraction from label references (HO) ) (c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/generic/gettitlestring/gettitlestring.sty @@ -312,27 +312,27 @@ Package: kvoptions 2022-06-15 v3.15 Key value format for package options (HO) \Hy@linkcounter=\count286 \Hy@pagecounter=\count287 (c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/hyperref/pd1enc.def -File: pd1enc.def 2023-04-22 v7.00x Hyperref: PDFDocEncoding definition (HO) +File: pd1enc.def 2023-05-16 v7.00y Hyperref: PDFDocEncoding definition (HO) ) (c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/generic/intcalc/intcalc.sty Package: intcalc 2019/12/15 v1.3 Expandable calculations with integers (HO) ) \Hy@SavedSpaceFactor=\count288 (c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/hyperref/puenc.def -File: puenc.def 2023-04-22 v7.00x Hyperref: PDF Unicode definition (HO) +File: puenc.def 2023-05-16 v7.00y Hyperref: PDF Unicode definition (HO) ) -Package hyperref Info: Hyper figures OFF on input line 4182. -Package hyperref Info: Link nesting OFF on input line 4187. -Package hyperref Info: Hyper index ON on input line 4190. -Package hyperref Info: Plain pages OFF on input line 4197. -Package hyperref Info: Backreferencing OFF on input line 4202. +Package hyperref Info: Hyper figures OFF on input line 4167. +Package hyperref Info: Link nesting OFF on input line 4172. +Package hyperref Info: Hyper index ON on input line 4175. +Package hyperref Info: Plain pages OFF on input line 4182. +Package hyperref Info: Backreferencing OFF on input line 4187. 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(c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/l3kernel/expl3.sty -Package: expl3 2023-05-05 L3 programming layer (loader) +Package: expl3 2023-06-05 L3 programming layer (loader) (c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/l3backend/l3backend-xetex.def File: l3backend-xetex.def 2023-04-19 L3 backend support: XeTeX \g__graphics_track_int=\count441 @@ -740,7 +740,7 @@ File: l3backend-xetex.def 2023-04-19 L3 backend support: XeTeX \g__pdf_backend_link_int=\count444 )) Package biblatex Info: ... and expl3 -(biblatex) 2023-05-05 L3 programming layer (loader) +(biblatex) 2023-06-05 L3 programming layer (loader) (biblatex) is new enough (at least 2020/04/06), (biblatex) setting 'casechanger=expl3'. (c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/biblatex/blx-case-expl3.sty (c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/l3packages/xparse/xparse.sty @@ -1064,6 +1064,9 @@ Package fancyhdr Warning: \headheight is too small (62.59596pt): (fancyhdr) \addtolength{\topmargin}{-1.71957pt}. [2] +LaTeX Font Info: Font shape `TU/lmtt/bx/n' in size <10> not available +(Font) Font shape `TU/lmtt/b/n' tried instead on input line 447. + Overfull \hbox (32.66139pt too wide) in paragraph at lines 463--463 []\TU/lmtt/m/n/10 #> -----------------------------------------------------------------------------[] [] @@ -1165,7 +1168,7 @@ Package fancyhdr Warning: \headheight is too small (62.59596pt): [10] Package hyperref Warning: Difference (2) between bookmark levels is greater -(hyperref) than one, level fixed on input line 973. +(hyperref) than one, level fixed on input line 974. File: D:/Rpackages/rticles/rmarkdown/templates/joss/resources/JOSE-logo.png Graphic file (type bmp) @@ -1177,17 +1180,17 @@ Package fancyhdr Warning: \headheight is too small (62.59596pt): (fancyhdr) \addtolength{\topmargin}{-1.71957pt}. [11] -Underfull \hbox (badness 1584) in paragraph at lines 1061--1067 +Underfull \hbox (badness 1584) in paragraph at lines 1062--1068 []\TU/lmr/m/n/10 Simmons, J. P., Nelson, L. D., & Simonsohn, U. (2011). False-positive psy- [] -Underfull \hbox (badness 3049) in paragraph at lines 1061--1067 +Underfull \hbox (badness 3049) in paragraph at lines 1062--1068 \TU/lmr/m/n/10 chology: Undisclosed flexibility in data collection and analysis allows pre- [] -Underfull \hbox (badness 3735) in paragraph at lines 1061--1067 +Underfull \hbox (badness 3735) in paragraph at lines 1062--1068 \TU/lmr/m/n/10 senting anything as significant. \TU/lmr/m/it/10 Psychological Science\TU/lmr/m/n/10 , \TU/lmr/m/it/10 22\TU/lmr/m/n/10 (11), 1359–1366. 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6e6a305284ccfa8b0a55f1d64d0020c0c531280d Mon Sep 17 00:00:00 2001 From: rempsyc Date: Fri, 16 Jun 2023 16:23:53 -0400 Subject: [PATCH 17/34] shorten paper [skip ci] --- papers/JOSE/paper.Rmd | 104 +---- papers/JOSE/paper.log | 96 ++--- papers/JOSE/paper.md | 150 +------- papers/JOSE/paper.pdf | Bin 241957 -> 197898 bytes .../JOSE/paper_files/figure-latex/model-1.pdf | Bin 8479 -> 8478 bytes .../paper_files/figure-latex/model2-1.pdf | Bin 9191 -> 9187 bytes .../figure-latex/multivariate_implicit-1.pdf | Bin 5785 -> 5785 bytes .../paper_files/figure-latex/scatter-1.pdf | Bin 8383 -> 8383 bytes .../figure-latex/univariate_implicit-1.pdf | Bin 5796 -> 5796 bytes papers/JOSE/paper_longform.Rmd | 354 ++++++++++++++++++ 10 files changed, 395 insertions(+), 309 deletions(-) create mode 100644 papers/JOSE/paper_longform.Rmd diff --git a/papers/JOSE/paper.Rmd b/papers/JOSE/paper.Rmd index 3214bde37..86dd99104 100644 --- a/papers/JOSE/paper.Rmd +++ b/papers/JOSE/paper.Rmd @@ -47,19 +47,6 @@ simplesummary: | The *{performance}* package from the *easystats* ecosystem makes it easy to diagnose outliers in R and according to current best practices thanks to the `check_outiers()` function. -abstract: | - Beyond the challenge of keeping up-to-date with current best practices - regarding the diagnosis and treatment of outliers, an additional difficulty - arises concerning the mathematical implementation of the recommended methods. - In this paper, we provide an overview of current recommendations and best - practices and demonstrate how they can easily and conveniently be - implemented in the R statistical computing software, using the *{performance}* - package of the *easystats* ecosystem. We cover univariate, multivariate, and - model-based statistical outlier detection methods, their recommended - threshold, standard output, and plotting methods. We conclude with - recommendations on the handling of outliers: the different theoretical types - of outliers, whether to exclude or winsorize them, and the importance of - transparency. keywords: | univariate outliers; multivariate outliers; robust detection methods; R; easystats acknowledgement: | @@ -116,6 +103,10 @@ library(see) library(datawizard) ``` +# Summary + +Beyond the challenge of keeping up-to-date with current best practices regarding the diagnosis and treatment of outliers, an additional difficulty arises concerning the mathematical implementation of the recommended methods. In this paper, we provide an overview of current recommendations and best practices and demonstrate how they can easily and conveniently be implemented in the R statistical computing software, using the *{performance}* package of the *easystats* ecosystem. We cover univariate, multivariate, and model-based statistical outlier detection methods, their recommended threshold, standard output, and plotting methods. We conclude with recommendations on the handling of outliers: the different theoretical types of outliers, whether to exclude or winsorize them, and the importance of transparency. + # Statement of Need Real-life data often contain observations that can be considered *abnormal* when compared to the main population. The cause of it---be it because they belong to a different distribution (originating from a different generative process) or simply being extreme cases, statistically rare but not impossible---can be hard to assess, and the boundaries of "abnormal" difficult to define. @@ -162,22 +153,7 @@ which(outliers) data_clean <- data[-which(outliers), ] ``` -All `check_outliers()` output objects possess a `plot()` method, meaning it is also possible to visualize the outliers: - -```{r univariate, eval=FALSE} -library(see) - -plot(outliers) -``` - -```{r univariate_implicit, fig.cap = "Visual depiction of outliers using the robust z-score method. The distance represents an aggregate score for variables mpg, cyl, disp, and hp.", echo=FALSE} -library(see) - -plot(outliers) + - ggplot2::theme(axis.text.x = ggplot2::element_text( - angle = 45, size = 7 -)) -``` +All `check_outliers()` output objects possess a `plot()` method, meaning it is also possible to visualize the outliers using the generic `plot()` function on the resulting outlier object after loading the {see} package. Other univariate methods are available, such as using the interquartile range (IQR), or based on different intervals, such as the Highest Density Interval (HDI) or the Bias Corrected and Accelerated Interval (BCI). These methods are documented and described in the function's [help page](). @@ -187,7 +163,7 @@ Univariate outliers can be useful when the focus is on a particular variable, fo However, in many scenarios, variables of a data set are not independent, and an abnormal observation will impact multiple dimensions. For instance, a participant giving random answers to a questionnaire. In this case, computing the _z_ score for each of the questions might not lead to satisfactory results. Instead, one might want to look at these variables together. -One common approach for this is to compute multivariate distance metrics such as the Mahalanobis distance. Although the Mahalanobis distance is very popular, just like the regular _z_ scores method, it is not robust and is heavily influenced by the outliers themselves. Therefore, for multivariate outliers, it is recommended to use the Minimum Covariance Determinant, a robust version of the Mahalanobis distance [MCD, @leys2018outliers; @leys2019outliers]. +One common approach for this is to compute multivariate distance metrics such as the Mahalanobis distance. Although the Mahalanobis distance is very popular, just like the regular _z_ scores method, it is not robust and is heavily influenced by the outliers themselves. Therefore, for multivariate outliers, it is recommended to use the Minimum Covariance Determinant, a robust version of the Mahalanobis distance [MCD, @leys2018outliers; @leys2019outliers]. In *{performance}*'s `check_outliers()`, one can use this approach with `method = "mcd"`.^[Our default threshold for the MCD method is defined by `stats::qchisq(p = 1 - 0.001, df = ncol(x))`, which again is an approximation of the critical value for _p_ < .001 consistent with the thresholds of our other methods.] @@ -196,17 +172,6 @@ outliers <- check_outliers(data, method = "mcd") outliers ``` -```{r multivariate_plot, eval=FALSE} -plot(outliers) -``` - -```{r multivariate_implicit, fig.cap = "Visual depiction of outliers using the Minimum Covariance Determinant (MCD) method, a robust version of the Mahalanobis distance. The distance represents the MCD scores for variables mpg, cyl, disp, and hp.", echo=FALSE} -plot(outliers) + - ggplot2::theme(axis.text.x = ggplot2::element_text( - angle = 45, size = 7 -)) -``` - Other multivariate methods are available, such as another type of robust Mahalanobis distance that in this case relies on an orthogonalized Gnanadesikan-Kettenring pairwise estimator [@gnanadesikan1972robust]. These methods are documented and described in the function's [help page](https://easystats.github.io/performance/reference/check_outliers.html). ## Model-Based Outliers @@ -251,30 +216,6 @@ knitr::kable( However, distribution-based approaches are not a silver bullet either, and there are cases where the usage of methods agnostic to theoretical and statistical models of interest might be problematic. For example, a very tall person would be expected to also be much heavier than average, but that would still fit with the expected association between height and weight (i.e., it would be in line with a model such as `weight ~ height`). In contrast, using multivariate outlier detection methods there may flag this person as being an outlier---being unusual on two variables, height and weight---even though the pattern fits perfectly with our predictions. -In the example below, we plot the raw data and see two possible outliers. The first one falls along the regression line, and is therefore "in line" with our hypothesis. The second one clearly diverges from the regression line, and therefore we can conclude that this outlier may have a disproportionate influence on our model. - -```{r scatter, fig.cap = "Scatter plot of height and weight, with two extreme observations: one model-consistent (top-right) and the other, model-inconsistent (i.e., an outlier; bottom-right)."} -data <- women[rep(seq_len(nrow(women)), each = 100), ] -data <- rbind(data, c(100, 258), c(100, 200)) -model <- lm(weight ~ height, data) -rempsyc::nice_scatter(data, "height", "weight") -``` - -Using either the *z*-score or MCD methods, our model-consistent observation will be incorrectly flagged as an outlier or influential observation. - -```{r} -outliers <- check_outliers(model, method = c("zscore_robust", "mcd")) -which(outliers) -``` - -In contrast, the model-based detection method displays the desired behaviour: it correctly flags the person who is very tall but very light, without flagging the person who is both tall and heavy. - -```{r model2, fig.cap = "The leverage method (Cook's distance) correctly distinguishes the true outlier from the model-consistent extreme observation), based on the fitted model."} -outliers <- check_outliers(model, method = "cook") -which(outliers) -plot(outliers) -``` - Finally, unusual observations happen naturally: extreme observations are expected even when taken from a normal distribution. While statistical models can integrate this "expectation", multivariate outlier methods might be too conservative, flagging too many observations despite belonging to the right generative process. For these reasons, we believe that model-based methods are still preferable to the MCD when using supported regression models. Additionally, if the presence of multiple outliers is a significant concern, regression methods that are more robust to outliers should be considered---like _t_ regression or quantile regression---as they render their precise identification less critical [@mcelreath2020statistical]. ## Composite Outlier Score @@ -316,39 +257,8 @@ _Removing_ outliers can in this case be a valid strategy, and ideally one would The _easystats_ ecosystem makes it easy to incorporate this step into your workflow through the `winsorize()` function of *{datawizard}*, a lightweight R package to facilitate data wrangling and statistical transformations [@patil2022datawizard]. This procedure will bring back univariate outliers within the limits of 'acceptable' values, based either on the percentile, the _z_ score, or its robust alternative based on the MAD. -```{r winsorization} -data[1501:1502, ] # See outliers rows - -# Winsorizing using the MAD -library(datawizard) -winsorized_data <- winsorize(data, method = "zscore", robust = TRUE, threshold = 3) - -# Values > +/- MAD have been winsorized -winsorized_data[1501:1502, ] -``` - ## The Importance of Transparency -Once again, it is a critical part of a sound outlier treatment that regardless of which SOD method used, it should be reported in a reproducible manner. Ideally, the handling of outliers should be specified *a priori* with as much detail as possible, and preregistered, to limit researchers' degrees of freedom and therefore risks of false positives [@leys2019outliers]. This is especially true given that interesting outliers and random outliers are often times hard to distinguish in practice. Thus, researchers should always prioritize transparency and report all of the following information: (a) how many outliers were identified (including percentage); (b) according to which method and criteria, (c) using which function of which R package (if applicable), and (d) how they were handled (excluded or winsorized, if the latter, using what threshold). If at all possible, (e) the corresponding code script along with the data should be shared on a public repository like the Open Science Framework (OSF), so that the exclusion criteria can be reproduced precisely. - -# Conclusion - -In this paper, we have showed how to investigate outliers using the `check_outliers()` function of the *{performance}* package while following current good practices. However, best practice for outlier treatment does not stop at using appropriate statistical algorithms, but entails respecting existing recommendations, such as preregistration, reproducibility, consistency, transparency, and justification. Ideally, one would additionally also report the package, function, and threshold used (linking to the full code when possible). We hope that this paper and the accompanying `check_outlier()` function of *easystats* will help researchers engage in good research practices while providing a smooth outlier detection experience. - -### Contributions - -R.T. drafted the paper; all authors contributed to both the writing of the paper and the conception of the software. - -### Acknowledgements - -*{performance}* is part of the collaborative [*easystats*](https://github.com/easystats/easystats) ecosystem [@easystatspackage]. Thus, we thank all [members of easystats](https://github.com/orgs/easystats/people), contributors, and users alike. - -### Funding information - -This research received no external funding. - -### Competing Interests - -The authors declare no conflict of interest +Finally, it is a critical part of a sound outlier treatment that regardless of which SOD method used, it should be reported in a reproducible manner. Ideally, the handling of outliers should be specified *a priori* with as much detail as possible, and preregistered, to limit researchers' degrees of freedom and therefore risks of false positives [@leys2019outliers]. This is especially true given that interesting outliers and random outliers are often times hard to distinguish in practice. Thus, researchers should always prioritize transparency and report all of the following information: (a) how many outliers were identified (including percentage); (b) according to which method and criteria, (c) using which function of which R package (if applicable), and (d) how they were handled (excluded or winsorized, if the latter, using what threshold). If at all possible, (e) the corresponding code script along with the data should be shared on a public repository like the Open Science Framework (OSF), so that the exclusion criteria can be reproduced precisely. # References \ No newline at end of file diff --git a/papers/JOSE/paper.log b/papers/JOSE/paper.log index d1524398a..30ce84931 100644 --- a/papers/JOSE/paper.log +++ b/papers/JOSE/paper.log @@ -1,4 +1,4 @@ -This is XeTeX, Version 3.141592653-2.6-0.999995 (TeX Live 2023) (preloaded format=xelatex 2023.6.8) 16 JUN 2023 15:11 +This is XeTeX, Version 3.141592653-2.6-0.999995 (TeX Live 2023) (preloaded format=xelatex 2023.6.8) 16 JUN 2023 16:14 entering extended mode restricted \write18 enabled. %&-line parsing enabled. @@ -1032,13 +1032,13 @@ File: umsb.fd 2013/01/14 v3.01 AMS symbols B File: mt-msb.cfg 2005/06/01 v1.0 microtype config. file: AMS symbols (b) (RS) ) -Package hyperref Warning: Suppressing link with empty target on input line 337. +Package hyperref Warning: Suppressing link with empty target on input line 322. -Package hyperref Warning: Suppressing link with empty target on input line 337. +Package hyperref Warning: Suppressing link with empty target on input line 322. -Package hyperref Warning: Suppressing link with empty target on input line 337. +Package hyperref Warning: Suppressing link with empty target on input line 322. File: D:/Rpackages/rticles/rmarkdown/templates/joss/resources/JOSE-logo.png Graphic file (type bmp) @@ -1050,7 +1050,7 @@ Package fancyhdr Warning: \headheight is too small (62.59596pt): (fancyhdr) \addtolength{\topmargin}{-1.71957pt}. LaTeX Font Info: Font shape `TU/lmss/m/it' in size <8> not available -(Font) Font shape `TU/lmss/m/sl' tried instead on input line 376. +(Font) Font shape `TU/lmss/m/sl' tried instead on input line 378. [1 ] @@ -1065,19 +1065,17 @@ Package fancyhdr Warning: \headheight is too small (62.59596pt): [2] LaTeX Font Info: Font shape `TU/lmtt/bx/n' in size <10> not available -(Font) Font shape `TU/lmtt/b/n' tried instead on input line 447. +(Font) Font shape `TU/lmtt/b/n' tried instead on input line 449. -Overfull \hbox (32.66139pt too wide) in paragraph at lines 463--463 +Overfull \hbox (32.66139pt too wide) in paragraph at lines 465--465 []\TU/lmtt/m/n/10 #> -----------------------------------------------------------------------------[] [] -Overfull \hbox (32.66139pt too wide) in paragraph at lines 472--472 +Overfull \hbox (32.66139pt too wide) in paragraph at lines 474--474 []\TU/lmtt/m/n/10 #> -----------------------------------------------------------------------------[] [] -File: paper_files/figure-latex/univariate_implicit-1.pdf Graphic file (type pdf) - File: D:/Rpackages/rticles/rmarkdown/templates/joss/resources/JOSE-logo.png Graphic file (type bmp) @@ -1098,8 +1096,8 @@ Package fancyhdr Warning: \headheight is too small (62.59596pt): (fancyhdr) \addtolength{\topmargin}{-1.71957pt}. [4] -File: paper_files/figure-latex/multivariate_implicit-1.pdf Graphic file (type pdf) - +File: paper_files/figure-latex/model-1.pdf Graphic file (type pdf) + File: D:/Rpackages/rticles/rmarkdown/templates/joss/resources/JOSE-logo.png Graphic file (type bmp) @@ -1110,8 +1108,6 @@ Package fancyhdr Warning: \headheight is too small (62.59596pt): (fancyhdr) \addtolength{\topmargin}{-1.71957pt}. [5] -File: paper_files/figure-latex/model-1.pdf Graphic file (type pdf) - File: D:/Rpackages/rticles/rmarkdown/templates/joss/resources/JOSE-logo.png Graphic file (type bmp) @@ -1122,8 +1118,6 @@ Package fancyhdr Warning: \headheight is too small (62.59596pt): (fancyhdr) \addtolength{\topmargin}{-1.71957pt}. [6] -File: paper_files/figure-latex/scatter-1.pdf Graphic file (type pdf) - File: D:/Rpackages/rticles/rmarkdown/templates/joss/resources/JOSE-logo.png Graphic file (type bmp) @@ -1134,63 +1128,17 @@ Package fancyhdr Warning: \headheight is too small (62.59596pt): (fancyhdr) \addtolength{\topmargin}{-1.71957pt}. [7] -File: paper_files/figure-latex/model2-1.pdf Graphic file (type pdf) - -File: D:/Rpackages/rticles/rmarkdown/templates/joss/resources/JOSE-logo.png Graphic file (type bmp) - - -Package fancyhdr Warning: \headheight is too small (62.59596pt): -(fancyhdr) Make it at least 64.31554pt, for example: -(fancyhdr) \setlength{\headheight}{64.31554pt}. -(fancyhdr) You might also make \topmargin smaller to compensate: -(fancyhdr) \addtolength{\topmargin}{-1.71957pt}. - -[8] -File: D:/Rpackages/rticles/rmarkdown/templates/joss/resources/JOSE-logo.png Graphic file (type bmp) - - -Package fancyhdr Warning: \headheight is too small (62.59596pt): -(fancyhdr) Make it at least 64.31554pt, for example: -(fancyhdr) \setlength{\headheight}{64.31554pt}. -(fancyhdr) You might also make \topmargin smaller to compensate: -(fancyhdr) \addtolength{\topmargin}{-1.71957pt}. - -[9] -File: D:/Rpackages/rticles/rmarkdown/templates/joss/resources/JOSE-logo.png Graphic file (type bmp) - - -Package fancyhdr Warning: \headheight is too small (62.59596pt): -(fancyhdr) Make it at least 64.31554pt, for example: -(fancyhdr) \setlength{\headheight}{64.31554pt}. -(fancyhdr) You might also make \topmargin smaller to compensate: -(fancyhdr) \addtolength{\topmargin}{-1.71957pt}. - -[10] - -Package hyperref Warning: Difference (2) between bookmark levels is greater -(hyperref) than one, level fixed on input line 974. - -File: D:/Rpackages/rticles/rmarkdown/templates/joss/resources/JOSE-logo.png Graphic file (type bmp) - - -Package fancyhdr Warning: \headheight is too small (62.59596pt): -(fancyhdr) Make it at least 64.31554pt, for example: -(fancyhdr) \setlength{\headheight}{64.31554pt}. -(fancyhdr) You might also make \topmargin smaller to compensate: -(fancyhdr) \addtolength{\topmargin}{-1.71957pt}. - -[11] -Underfull \hbox (badness 1584) in paragraph at lines 1062--1068 +Underfull \hbox (badness 1584) in paragraph at lines 910--916 []\TU/lmr/m/n/10 Simmons, J. P., Nelson, L. D., & Simonsohn, U. (2011). False-positive psy- [] -Underfull \hbox (badness 3049) in paragraph at lines 1062--1068 +Underfull \hbox (badness 3049) in paragraph at lines 910--916 \TU/lmr/m/n/10 chology: Undisclosed flexibility in data collection and analysis allows pre- [] -Underfull \hbox (badness 3735) in paragraph at lines 1062--1068 +Underfull \hbox (badness 3735) in paragraph at lines 910--916 \TU/lmr/m/n/10 senting anything as significant. \TU/lmr/m/it/10 Psychological Science\TU/lmr/m/n/10 , \TU/lmr/m/it/10 22\TU/lmr/m/n/10 (11), 1359–1366. [] @@ -1203,20 +1151,20 @@ Package fancyhdr Warning: \headheight is too small (62.59596pt): (fancyhdr) You might also make \topmargin smaller to compensate: (fancyhdr) \addtolength{\topmargin}{-1.71957pt}. -[12] (./paper.aux) +[8] (./paper.aux) Package rerunfilecheck Info: File `paper.out' has not changed. -(rerunfilecheck) Checksum: 95B8741FA43CE9FFCC8820051C14B1E3;2674. +(rerunfilecheck) Checksum: EEBE57815200557F8EDD73A1BF6F9118;2043. Package logreq Info: Writing requests to 'paper.run.xml'. \openout1 = `paper.run.xml'. ) Here is how much of TeX's memory you used: - 37341 strings out of 478641 - 771578 string characters out of 5846292 - 1873382 words of memory out of 5000000 - 56907 multiletter control sequences out of 15000+600000 - 520323 words of font info for 90 fonts, out of 8000000 for 9000 + 37274 strings out of 478641 + 768952 string characters out of 5846292 + 1872382 words of memory out of 5000000 + 56849 multiletter control sequences out of 15000+600000 + 520299 words of font info for 87 fonts, out of 8000000 for 9000 14 hyphenation exceptions out of 8191 - 84i,13n,81p,1194b,848s stack positions out of 10000i,1000n,20000p,200000b,200000s + 84i,12n,81p,1194b,848s stack positions out of 10000i,1000n,20000p,200000b,200000s -Output written on paper.pdf (12 pages). +Output written on paper.pdf (8 pages). diff --git a/papers/JOSE/paper.md b/papers/JOSE/paper.md index 518e33e75..b6c3946b9 100644 --- a/papers/JOSE/paper.md +++ b/papers/JOSE/paper.md @@ -47,19 +47,6 @@ simplesummary: | The *{performance}* package from the *easystats* ecosystem makes it easy to diagnose outliers in R and according to current best practices thanks to the `check_outiers()` function. -abstract: | - Beyond the challenge of keeping up-to-date with current best practices - regarding the diagnosis and treatment of outliers, an additional difficulty - arises concerning the mathematical implementation of the recommended methods. - In this paper, we provide an overview of current recommendations and best - practices and demonstrate how they can easily and conveniently be - implemented in the R statistical computing software, using the *{performance}* - package of the *easystats* ecosystem. We cover univariate, multivariate, and - model-based statistical outlier detection methods, their recommended - threshold, standard output, and plotting methods. We conclude with - recommendations on the handling of outliers: the different theoretical types - of outliers, whether to exclude or winsorize them, and the importance of - transparency. keywords: | univariate outliers; multivariate outliers; robust detection methods; R; easystats acknowledgement: | @@ -104,6 +91,10 @@ csl: apa.csl +# Summary + +Beyond the challenge of keeping up-to-date with current best practices regarding the diagnosis and treatment of outliers, an additional difficulty arises concerning the mathematical implementation of the recommended methods. In this paper, we provide an overview of current recommendations and best practices and demonstrate how they can easily and conveniently be implemented in the R statistical computing software, using the *{performance}* package of the *easystats* ecosystem. We cover univariate, multivariate, and model-based statistical outlier detection methods, their recommended threshold, standard output, and plotting methods. We conclude with recommendations on the handling of outliers: the different theoretical types of outliers, whether to exclude or winsorize them, and the importance of transparency. + # Statement of Need Real-life data often contain observations that can be considered *abnormal* when compared to the main population. The cause of it---be it because they belong to a different distribution (originating from a different generative process) or simply being extreme cases, statistically rare but not impossible---can be hard to assess, and the boundaries of "abnormal" difficult to define. @@ -186,18 +177,7 @@ which(outliers) data_clean <- data[-which(outliers), ] ``` -All `check_outliers()` output objects possess a `plot()` method, meaning it is also possible to visualize the outliers: - - -```r -library(see) - -plot(outliers) -``` - -\begin{figure} -\includegraphics[width=1\linewidth]{paper_files/figure-latex/univariate_implicit-1} \caption{Visual depiction of outliers using the robust z-score method. The distance represents an aggregate score for variables mpg, cyl, disp, and hp.}\label{fig:univariate_implicit} -\end{figure} +All `check_outliers()` output objects possess a `plot()` method, meaning it is also possible to visualize the outliers using the generic `plot()` function on the resulting outlier object after loading the {see} package. Other univariate methods are available, such as using the interquartile range (IQR), or based on different intervals, such as the Highest Density Interval (HDI) or the Bias Corrected and Accelerated Interval (BCI). These methods are documented and described in the function's [help page](). @@ -207,7 +187,7 @@ Univariate outliers can be useful when the focus is on a particular variable, fo However, in many scenarios, variables of a data set are not independent, and an abnormal observation will impact multiple dimensions. For instance, a participant giving random answers to a questionnaire. In this case, computing the _z_ score for each of the questions might not lead to satisfactory results. Instead, one might want to look at these variables together. -One common approach for this is to compute multivariate distance metrics such as the Mahalanobis distance. Although the Mahalanobis distance is very popular, just like the regular _z_ scores method, it is not robust and is heavily influenced by the outliers themselves. Therefore, for multivariate outliers, it is recommended to use the Minimum Covariance Determinant, a robust version of the Mahalanobis distance [MCD, @leys2018outliers; @leys2019outliers]. +One common approach for this is to compute multivariate distance metrics such as the Mahalanobis distance. Although the Mahalanobis distance is very popular, just like the regular _z_ scores method, it is not robust and is heavily influenced by the outliers themselves. Therefore, for multivariate outliers, it is recommended to use the Minimum Covariance Determinant, a robust version of the Mahalanobis distance [MCD, @leys2018outliers; @leys2019outliers]. In *{performance}*'s `check_outliers()`, one can use this approach with `method = "mcd"`.^[Our default threshold for the MCD method is defined by `stats::qchisq(p = 1 - 0.001, df = ncol(x))`, which again is an approximation of the critical value for _p_ < .001 consistent with the thresholds of our other methods.] @@ -223,15 +203,6 @@ outliers #> - For variables: mpg, cyl, disp, hp. ``` - -```r -plot(outliers) -``` - -\begin{figure} -\includegraphics[width=1\linewidth]{paper_files/figure-latex/multivariate_implicit-1} \caption{Visual depiction of outliers using the Minimum Covariance Determinant (MCD) method, a robust version of the Mahalanobis distance. The distance represents the MCD scores for variables mpg, cyl, disp, and hp.}\label{fig:multivariate_implicit} -\end{figure} - Other multivariate methods are available, such as another type of robust Mahalanobis distance that in this case relies on an orthogonalized Gnanadesikan-Kettenring pairwise estimator [@gnanadesikan1972robust]. These methods are documented and described in the function's [help page](https://easystats.github.io/performance/reference/check_outliers.html). ## Model-Based Outliers @@ -278,52 +249,6 @@ Table: Summary of Statistical Outlier Detection Methods Recommendations. However, distribution-based approaches are not a silver bullet either, and there are cases where the usage of methods agnostic to theoretical and statistical models of interest might be problematic. For example, a very tall person would be expected to also be much heavier than average, but that would still fit with the expected association between height and weight (i.e., it would be in line with a model such as `weight ~ height`). In contrast, using multivariate outlier detection methods there may flag this person as being an outlier---being unusual on two variables, height and weight---even though the pattern fits perfectly with our predictions. -In the example below, we plot the raw data and see two possible outliers. The first one falls along the regression line, and is therefore "in line" with our hypothesis. The second one clearly diverges from the regression line, and therefore we can conclude that this outlier may have a disproportionate influence on our model. - - -```r -data <- women[rep(seq_len(nrow(women)), each = 100), ] -data <- rbind(data, c(100, 258), c(100, 200)) -model <- lm(weight ~ height, data) -rempsyc::nice_scatter(data, "height", "weight") -``` - -\begin{figure} -\includegraphics[width=1\linewidth]{paper_files/figure-latex/scatter-1} \caption{Scatter plot of height and weight, with two extreme observations: one model-consistent (top-right) and the other, model-inconsistent (i.e., an outlier; bottom-right).}\label{fig:scatter} -\end{figure} - -Using either the *z*-score or MCD methods, our model-consistent observation will be incorrectly flagged as an outlier or influential observation. - - -```r -outliers <- check_outliers(model, method = c("zscore_robust", "mcd")) -which(outliers) -``` - -``` -#> [1] 1501 1502 -``` - -In contrast, the model-based detection method displays the desired behaviour: it correctly flags the person who is very tall but very light, without flagging the person who is both tall and heavy. - - -```r -outliers <- check_outliers(model, method = "cook") -which(outliers) -``` - -``` -#> [1] 1502 -``` - -```r -plot(outliers) -``` - -\begin{figure} -\includegraphics[width=1\linewidth]{paper_files/figure-latex/model2-1} \caption{The leverage method (Cook's distance) correctly distinguishes the true outlier from the model-consistent extreme observation), based on the fitted model.}\label{fig:model2} -\end{figure} - Finally, unusual observations happen naturally: extreme observations are expected even when taken from a normal distribution. While statistical models can integrate this "expectation", multivariate outlier methods might be too conservative, flagging too many observations despite belonging to the right generative process. For these reasons, we believe that model-based methods are still preferable to the MCD when using supported regression models. Additionally, if the presence of multiple outliers is a significant concern, regression methods that are more robust to outliers should be considered---like _t_ regression or quantile regression---as they render their precise identification less critical [@mcelreath2020statistical]. ## Composite Outlier Score @@ -339,7 +264,7 @@ which(outliers) ``` ``` -#> [1] 1501 1502 +#> [1] 33 34 ``` Outliers (counts or per variables) for individual methods can then be obtained through attributes. For example: @@ -350,15 +275,10 @@ attributes(outliers)$outlier_var$zscore_robust ``` ``` -#> $weight -#> Row Distance_Zscore_robust -#> 1501 1501 6.913530 -#> 1502 1502 3.653492 -#> -#> $height -#> Row Distance_Zscore_robust -#> 1501 1501 5.901794 -#> 1502 1502 5.901794 +#> $mpg +#> Row Distance_Zscore_robust +#> 33 33 3.709699 +#> 34 34 5.848328 ``` An example sentence for reporting the usage of the composite method could be: @@ -383,54 +303,8 @@ _Removing_ outliers can in this case be a valid strategy, and ideally one would The _easystats_ ecosystem makes it easy to incorporate this step into your workflow through the `winsorize()` function of *{datawizard}*, a lightweight R package to facilitate data wrangling and statistical transformations [@patil2022datawizard]. This procedure will bring back univariate outliers within the limits of 'acceptable' values, based either on the percentile, the _z_ score, or its robust alternative based on the MAD. - -```r -data[1501:1502, ] # See outliers rows -``` - -``` -#> height weight -#> 1501 100 258 -#> 1502 100 200 -``` - -```r -# Winsorizing using the MAD -library(datawizard) -winsorized_data <- winsorize(data, method = "zscore", robust = TRUE, threshold = 3) - -# Values > +/- MAD have been winsorized -winsorized_data[1501:1502, ] -``` - -``` -#> height weight -#> 1501 82.7912 188.3736 -#> 1502 82.7912 188.3736 -``` - ## The Importance of Transparency -Once again, it is a critical part of a sound outlier treatment that regardless of which SOD method used, it should be reported in a reproducible manner. Ideally, the handling of outliers should be specified *a priori* with as much detail as possible, and preregistered, to limit researchers' degrees of freedom and therefore risks of false positives [@leys2019outliers]. This is especially true given that interesting outliers and random outliers are often times hard to distinguish in practice. Thus, researchers should always prioritize transparency and report all of the following information: (a) how many outliers were identified (including percentage); (b) according to which method and criteria, (c) using which function of which R package (if applicable), and (d) how they were handled (excluded or winsorized, if the latter, using what threshold). If at all possible, (e) the corresponding code script along with the data should be shared on a public repository like the Open Science Framework (OSF), so that the exclusion criteria can be reproduced precisely. - -# Conclusion - -In this paper, we have showed how to investigate outliers using the `check_outliers()` function of the *{performance}* package while following current good practices. However, best practice for outlier treatment does not stop at using appropriate statistical algorithms, but entails respecting existing recommendations, such as preregistration, reproducibility, consistency, transparency, and justification. Ideally, one would additionally also report the package, function, and threshold used (linking to the full code when possible). We hope that this paper and the accompanying `check_outlier()` function of *easystats* will help researchers engage in good research practices while providing a smooth outlier detection experience. - -### Contributions - -R.T. drafted the paper; all authors contributed to both the writing of the paper and the conception of the software. - -### Acknowledgements - -*{performance}* is part of the collaborative [*easystats*](https://github.com/easystats/easystats) ecosystem [@easystatspackage]. Thus, we thank all [members of easystats](https://github.com/orgs/easystats/people), contributors, and users alike. - -### Funding information - -This research received no external funding. - -### Competing Interests - -The authors declare no conflict of interest +Finally, it is a critical part of a sound outlier treatment that regardless of which SOD method used, it should be reported in a reproducible manner. Ideally, the handling of outliers should be specified *a priori* with as much detail as possible, and preregistered, to limit researchers' degrees of freedom and therefore risks of false positives [@leys2019outliers]. This is especially true given that interesting outliers and random outliers are often times hard to distinguish in practice. Thus, researchers should always prioritize transparency and report all of the following information: (a) how many outliers were identified (including percentage); (b) according to which method and criteria, (c) using which function of which R package (if applicable), and (d) how they were handled (excluded or winsorized, if the latter, using what threshold). If at all possible, (e) the corresponding code script along with the data should be shared on a public repository like the Open Science Framework (OSF), so that the exclusion criteria can be reproduced precisely. # References diff --git a/papers/JOSE/paper.pdf b/papers/JOSE/paper.pdf index 32cf8d55f9cdf009689025ed540385a38849a25f..f3c3372a63f712d83bb9868f375a624fe19b01a2 100644 GIT binary patch delta 71233 zcmZUaW0NjQ6kf-+ZQJ%4+qR7}<~z1++qP}nwt2?6Nu^Rrr9XA=AF#WhwO5xMB1A^Q z`8NZf3Z$VdgOCH*n7LR41Yn$9{+b!t!FX)m;7!Gnwmsz5ofBeZ-a!&g6HD5XwZ&kL z6OS9QHD(Xhf}S1jA!?0~MA=GP-%tR9(7A;qteZBBdub%}e0NsJodT?3yD1jbf-t`#u3n79HOQd0S!l(eHP6g7$m9 zbsXry>ez#0SE<$E0z)uTlIU%5X?;1x%MQw!Hb3WI-*hD}b&TQ}Uu6F@ZXONFil5WI z5>6sc>8ao1-iw^N)818jyVfwPL~bi!hGB*2zHRX}K6qX}3VnqSBY|K+fK-pjd@Zf$ zcX)~P5-0%v{-RWtZxPe)FL#8$*=gW>$Tv=4^|h@9I2s4RD?9 zcq^{(Dz4e{pLgCulf=o%yXV450>Rmc%AELF2R$c2j^hZ|RNb>Cr(EToD`|5&6qYdB zyS>*$vLC5o??ZG2NLZ68&8$-I+xHuNE62m=!_ff6G^nEVF40-&qhx`#HhsXTw1FG? 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For instance, a participant giving random answers to a questionnaire. In this case, computing the _z_ score for each of the questions might not lead to satisfactory results. Instead, one might want to look at these variables together. + +One common approach for this is to compute multivariate distance metrics such as the Mahalanobis distance. Although the Mahalanobis distance is very popular, just like the regular _z_ scores method, it is not robust and is heavily influenced by the outliers themselves. Therefore, for multivariate outliers, it is recommended to use the Minimum Covariance Determinant, a robust version of the Mahalanobis distance [MCD, @leys2018outliers; @leys2019outliers]. + +In *{performance}*'s `check_outliers()`, one can use this approach with `method = "mcd"`.^[Our default threshold for the MCD method is defined by `stats::qchisq(p = 1 - 0.001, df = ncol(x))`, which again is an approximation of the critical value for _p_ < .001 consistent with the thresholds of our other methods.] + +```{r multivariate} +outliers <- check_outliers(data, method = "mcd") +outliers +``` + +```{r multivariate_plot, eval=FALSE} +plot(outliers) +``` + +```{r multivariate_implicit, fig.cap = "Visual depiction of outliers using the Minimum Covariance Determinant (MCD) method, a robust version of the Mahalanobis distance. The distance represents the MCD scores for variables mpg, cyl, disp, and hp.", echo=FALSE} +plot(outliers) + + ggplot2::theme(axis.text.x = ggplot2::element_text( + angle = 45, size = 7 +)) +``` + +Other multivariate methods are available, such as another type of robust Mahalanobis distance that in this case relies on an orthogonalized Gnanadesikan-Kettenring pairwise estimator [@gnanadesikan1972robust]. These methods are documented and described in the function's [help page](https://easystats.github.io/performance/reference/check_outliers.html). + +## Model-Based Outliers + +Working with regression models creates the possibility of using model-based SOD methods. These methods rely on the concept of *leverage*, that is, how much influence a given observation can have on the model estimates. If few observations have a relatively strong leverage/influence on the model, one can suspect that the model's estimates are biased by these observations, in which case flagging them as outliers could prove helpful (see next section, "Handling Outliers"). + +In {performance}, two such model-based SOD methods are currently available: Cook's distance, for regular regression models, and Pareto, for Bayesian models. As such, `check_outliers()` can be applied directly on regression model objects, by simply specifying `method = "cook"` (or `method = "pareto"` for Bayesian models).^[Our default threshold for the Cook method is defined by `stats::qf(0.5, ncol(x), nrow(x) - ncol(x))`, which again is an approximation of the critical value for _p_ < .001 consistent with the thresholds of our other methods.] + +```{r model, fig.cap = "Visual depiction of outliers based on Cook's distance (leverage and standardized residuals), based on the fitted model."} +model <- lm(disp ~ mpg * disp, data = data) +outliers <- check_outliers(model, method = "cook") +outliers + +plot(outliers) +``` + +Table 1 below summarizes which methods to use in which cases, and with what threshold. + +```{r, echo=FALSE} +df <- data.frame( + `Statistical Test` = c( + "Supported regression model", + "Structural Equation Modeling (or other unsupported model)", + "Simple test with few variables (*t* test, correlation, etc.)"), + `Diagnosis Method` = c( + "**Model-based**: Cook (or Pareto for Bayesian models)", + "**Multivariate**: Minimum Covariance Determinant (MCD)", + "**Univariate**: robust *z* scores (MAD)"), + `Recommended Threshold` = c( + "`qf(0.5, ncol(x), nrow(x) - ncol(x))` (or 0.7 for Pareto)", + "`qchisq(p = 1 - 0.001, df = ncol(x))`", + "`qnorm(p = 1 - 0.001 / 2)`, ~ 3.29") +) +knitr::kable( + df, col.names = gsub("[.]", " ", names(df)), + caption = "Summary of Statistical Outlier Detection Methods Recommendations.", longtable = TRUE) +``` + +## Cook's Distance vs. MCD + +@leys2018outliers report a preference for the MCD method over Cook's distance. This is because Cook's distance removes one observation at a time and checks its corresponding influence on the model each time [@cook1977detection], and flags any observation that has a large influence. In the view of these authors, when there are several outliers, the process of removing a single outlier at a time is problematic as the model remains "contaminated" or influenced by other possible outliers in the model, rendering this method suboptimal in the presence of multiple outliers. + +However, distribution-based approaches are not a silver bullet either, and there are cases where the usage of methods agnostic to theoretical and statistical models of interest might be problematic. For example, a very tall person would be expected to also be much heavier than average, but that would still fit with the expected association between height and weight (i.e., it would be in line with a model such as `weight ~ height`). In contrast, using multivariate outlier detection methods there may flag this person as being an outlier---being unusual on two variables, height and weight---even though the pattern fits perfectly with our predictions. + +In the example below, we plot the raw data and see two possible outliers. The first one falls along the regression line, and is therefore "in line" with our hypothesis. The second one clearly diverges from the regression line, and therefore we can conclude that this outlier may have a disproportionate influence on our model. + +```{r scatter, fig.cap = "Scatter plot of height and weight, with two extreme observations: one model-consistent (top-right) and the other, model-inconsistent (i.e., an outlier; bottom-right)."} +data <- women[rep(seq_len(nrow(women)), each = 100), ] +data <- rbind(data, c(100, 258), c(100, 200)) +model <- lm(weight ~ height, data) +rempsyc::nice_scatter(data, "height", "weight") +``` + +Using either the *z*-score or MCD methods, our model-consistent observation will be incorrectly flagged as an outlier or influential observation. + +```{r} +outliers <- check_outliers(model, method = c("zscore_robust", "mcd")) +which(outliers) +``` + +In contrast, the model-based detection method displays the desired behaviour: it correctly flags the person who is very tall but very light, without flagging the person who is both tall and heavy. + +```{r model2, fig.cap = "The leverage method (Cook's distance) correctly distinguishes the true outlier from the model-consistent extreme observation), based on the fitted model."} +outliers <- check_outliers(model, method = "cook") +which(outliers) +plot(outliers) +``` + +Finally, unusual observations happen naturally: extreme observations are expected even when taken from a normal distribution. While statistical models can integrate this "expectation", multivariate outlier methods might be too conservative, flagging too many observations despite belonging to the right generative process. For these reasons, we believe that model-based methods are still preferable to the MCD when using supported regression models. Additionally, if the presence of multiple outliers is a significant concern, regression methods that are more robust to outliers should be considered---like _t_ regression or quantile regression---as they render their precise identification less critical [@mcelreath2020statistical]. + +## Composite Outlier Score + +The *{performance}* package also offers an alternative, consensus-based approach that combines several methods, based on the assumption that different methods provide different angles of looking at a given problem. By applying a variety of methods, one can hope to "triangulate" the true outliers (those consistently flagged by multiple methods) and thus attempt to minimize false positives. + +In practice, this approach computes a composite outlier score, formed of the average of the binary (0 or 1) classification results of each method. It represents the probability that each observation is classified as an outlier by at least one method. The default decision rule classifies rows with composite outlier scores superior or equal to 0.5 as outlier observations (i.e., that were classified as outliers by at least half of the methods). In *{performance}*'s `check_outliers()`, one can use this approach by including all desired methods in the corresponding argument. + +```{r multimethod, fig.cap = "Visual depiction of outliers using several different statistical outlier detection methods."} +outliers <- check_outliers(model, method = c("zscore_robust", "mcd", "cook")) +which(outliers) +``` + +Outliers (counts or per variables) for individual methods can then be obtained through attributes. For example: + +```{r} +attributes(outliers)$outlier_var$zscore_robust +``` + +An example sentence for reporting the usage of the composite method could be: + +> Based on a composite outlier score [see the 'check_outliers()' function in the 'performance' R package, @ludecke2021performance] obtained via the joint application of multiple outliers detection algorithms [(a) median absolute deviation (MAD)-based robust _z_ scores, @leys2013outliers; (b) Mahalanobis minimum covariance determinant (MCD), @leys2019outliers; and (c) Cook's distance, @cook1977detection], we excluded two participants that were classified as outliers by at least half of the methods used. + +# Handling Outliers + +The above section demonstrated how to identify outliers using the `check_outliers()` function in the *{performance}* package. But what should we do with these outliers once identified? Although it is common to automatically discard any observation that has been marked as "an outlier" as if it might infect the rest of the data with its statistical ailment, we believe that the use of SOD methods is but one step in the get-to-know-your-data pipeline; a researcher or analyst's _domain knowledge_ must be involved in the decision of how to deal with observations marked as outliers by means of SOD. Indeed, automatic tools can help detect outliers, but they are nowhere near perfect. Although they can be useful to flag suspect data, they can have misses and false alarms, and they cannot replace human eyes and proper vigilance from the researcher. If you do end up manually inspecting your data for outliers, it can be helpful to think of outliers as belonging to different types of outliers, or categories, which can help decide what to do with a given outlier. + +## Error, Interesting, and Random Outliers + +@leys2019outliers distinguish between error outliers, interesting outliers, and random outliers. _Error outliers_ are likely due to human error and should be corrected before data analysis or outright removed since they are invalid observations. _Interesting outliers_ are not due to technical error and may be of theoretical interest; it might thus be relevant to investigate them further even though they should be removed from the current analysis of interest. _Random outliers_ are assumed to be due to chance alone and to belong to the correct distribution and, therefore, should be retained. + +It is recommended to _keep_ observations which are expected to be part of the distribution of interest, even if they are outliers [@leys2019outliers]. However, if it is suspected that the outliers belong to an alternative distribution, then those observations could have a large impact on the results and call into question their robustness, especially if significance is conditional on their inclusion, so should be removed. + +On the other hand, there are also outliers that cannot be detected by statistical tools, but should be found and removed. For example, if we are studying the effects of X on Y among teenagers and we have one observation from a 20-year-old, this observation might not be a _statistical outlier_, but it is an outlier in the _context_ of our research, and should be discarded to allow for valid inferences. + +## Winsorization + +_Removing_ outliers can in this case be a valid strategy, and ideally one would report results with and without outliers to see the extent of their impact on results. This approach however can reduce statistical power. Therefore, some propose a _recoding_ approach, namely, winsorization: bringing outliers back within acceptable limits [e.g., 3 MADs, @tukey1963less]. However, if possible, it is recommended to collect enough data so that even after removing outliers, there is still sufficient statistical power without having to resort to winsorization [@leys2019outliers]. + +The _easystats_ ecosystem makes it easy to incorporate this step into your workflow through the `winsorize()` function of *{datawizard}*, a lightweight R package to facilitate data wrangling and statistical transformations [@patil2022datawizard]. This procedure will bring back univariate outliers within the limits of 'acceptable' values, based either on the percentile, the _z_ score, or its robust alternative based on the MAD. + +```{r winsorization} +data[1501:1502, ] # See outliers rows + +# Winsorizing using the MAD +library(datawizard) +winsorized_data <- winsorize(data, method = "zscore", robust = TRUE, threshold = 3) + +# Values > +/- MAD have been winsorized +winsorized_data[1501:1502, ] +``` + +## The Importance of Transparency + +Once again, it is a critical part of a sound outlier treatment that regardless of which SOD method used, it should be reported in a reproducible manner. Ideally, the handling of outliers should be specified *a priori* with as much detail as possible, and preregistered, to limit researchers' degrees of freedom and therefore risks of false positives [@leys2019outliers]. This is especially true given that interesting outliers and random outliers are often times hard to distinguish in practice. Thus, researchers should always prioritize transparency and report all of the following information: (a) how many outliers were identified (including percentage); (b) according to which method and criteria, (c) using which function of which R package (if applicable), and (d) how they were handled (excluded or winsorized, if the latter, using what threshold). If at all possible, (e) the corresponding code script along with the data should be shared on a public repository like the Open Science Framework (OSF), so that the exclusion criteria can be reproduced precisely. + +# Conclusion + +In this paper, we have showed how to investigate outliers using the `check_outliers()` function of the *{performance}* package while following current good practices. However, best practice for outlier treatment does not stop at using appropriate statistical algorithms, but entails respecting existing recommendations, such as preregistration, reproducibility, consistency, transparency, and justification. Ideally, one would additionally also report the package, function, and threshold used (linking to the full code when possible). We hope that this paper and the accompanying `check_outlier()` function of *easystats* will help researchers engage in good research practices while providing a smooth outlier detection experience. + +### Contributions + +R.T. drafted the paper; all authors contributed to both the writing of the paper and the conception of the software. + +### Acknowledgements + +*{performance}* is part of the collaborative [*easystats*](https://github.com/easystats/easystats) ecosystem [@easystatspackage]. Thus, we thank all [members of easystats](https://github.com/orgs/easystats/people), contributors, and users alike. + +### Funding information + +This research received no external funding. + +### Competing Interests + +The authors declare no conflict of interest + +# References \ No newline at end of file From aa30ec14fe98750d47a53fbce2b0191a9a3ad31e Mon Sep 17 00:00:00 2001 From: rempsyc Date: Fri, 16 Jun 2023 16:30:07 -0400 Subject: [PATCH 18/34] avoid name conflict with JOSS paper.bib [skip ci] --- papers/JOSS/{paper.bib => paper_temp.bib} | 0 1 file changed, 0 insertions(+), 0 deletions(-) rename papers/JOSS/{paper.bib => paper_temp.bib} (100%) diff --git a/papers/JOSS/paper.bib b/papers/JOSS/paper_temp.bib similarity index 100% rename from papers/JOSS/paper.bib rename to papers/JOSS/paper_temp.bib From 080fab5c460b4ae61cdf2db0ece5eb31593083e7 Mon Sep 17 00:00:00 2001 From: rempsyc Date: Fri, 16 Jun 2023 16:30:07 -0400 Subject: [PATCH 19/34] avoid name conflict with JOSS paper.bib --- papers/JOSS/{paper.bib => paper_temp.bib} | 0 1 file changed, 0 insertions(+), 0 deletions(-) rename papers/JOSS/{paper.bib => paper_temp.bib} (100%) diff --git a/papers/JOSS/paper.bib b/papers/JOSS/paper_temp.bib similarity index 100% rename from papers/JOSS/paper.bib rename to papers/JOSS/paper_temp.bib From c320527910d58e64017e1b7d8cbcb2cd744a7bf9 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?R=C3=A9mi=20Th=C3=A9riault?= <13123390+rempsyc@users.noreply.github.com> Date: Wed, 27 Sep 2023 19:15:48 -0400 Subject: [PATCH 20/34] fixes #619 --- papers/JOSE/paper.Rmd | 7 +- papers/JOSE/paper.log | 698 ++++++++++++------ papers/JOSE/paper.md | 7 +- papers/JOSE/paper.pdf | Bin 197898 -> 195839 bytes .../JOSE/paper_files/figure-latex/model-1.pdf | Bin 8478 -> 5757 bytes 5 files changed, 479 insertions(+), 233 deletions(-) diff --git a/papers/JOSE/paper.Rmd b/papers/JOSE/paper.Rmd index 86dd99104..d2b4dbfe7 100644 --- a/papers/JOSE/paper.Rmd +++ b/papers/JOSE/paper.Rmd @@ -111,10 +111,11 @@ Beyond the challenge of keeping up-to-date with current best practices regarding Real-life data often contain observations that can be considered *abnormal* when compared to the main population. The cause of it---be it because they belong to a different distribution (originating from a different generative process) or simply being extreme cases, statistically rare but not impossible---can be hard to assess, and the boundaries of "abnormal" difficult to define. -Nonetheless, the improper handling of these outliers can substantially affect statistical model estimations, biasing effect estimations and weakening the models' predictive performance. -It is thus essential to address this problem in a thoughtful manner. Yet, despite the existence of established recommendations and guidelines, many researchers still do not treat outliers in a consistent manner, or do so using inappropriate strategies [@simmons2011false; @leys2013outliers]. +Nonetheless, the improper handling of these outliers can substantially affect statistical model estimations, biasing effect estimations and weakening the models' predictive performance. It is thus essential to address this problem in a thoughtful manner. Yet, despite the existence of established recommendations and guidelines, many researchers still do not treat outliers in a consistent manner, or do so using inappropriate strategies [@simmons2011false; @leys2013outliers]. -One possible reason is that researchers are not aware of the existing recommendations, or do not know how to implement them using their analysis software. In this paper, we show how to follow current best practices for automatic and reproducible statistical outlier detection (SOD) using R and the *{performance}* package [@ludecke2021performance], which is part of the *easystats* ecosystem of packages that build an R framework for easy statistical modeling, visualization, and reporting [@easystatspackage]. +One possible reason is that researchers are not aware of the existing recommendations, or do not know how to implement them using their analysis software. In this paper, we show how to follow current best practices for automatic and reproducible statistical outlier detection (SOD) using R and the *{performance}* package [@ludecke2021performance], which is part of the *easystats* ecosystem of packages that build an R framework for easy statistical modeling, visualization, and reporting [@easystatspackage]. Installation instructions can be found on [GitHub](https://github.com/easystats/performance) or its [website](https://easystats.github.io/performance/), and its list of dependencies on [CRAN](https://cran.r-project.org/package=performance). + +The instructional materials that follow is aimed at an audience of researchers who want to follow good practices, and is appropriate for advanced undergraduate students, graduate students, professors, or professionals having to deal with the nuances of outlier treatment. # Identifying Outliers diff --git a/papers/JOSE/paper.log b/papers/JOSE/paper.log index 30ce84931..046bb99c4 100644 --- a/papers/JOSE/paper.log +++ b/papers/JOSE/paper.log @@ -1,13 +1,14 @@ -This is XeTeX, Version 3.141592653-2.6-0.999995 (TeX Live 2023) (preloaded format=xelatex 2023.6.8) 16 JUN 2023 16:14 +This is XeTeX, Version 3.141592653-2.6-0.999995 (MiKTeX 23.5) (preloaded format=xelatex 2023.5.20) 27 SEP 2023 19:13 entering extended mode restricted \write18 enabled. %&-line parsing enabled. -**paper.tex -(./paper.tex +**./paper.tex +(paper.tex LaTeX2e <2022-11-01> patch level 1 -L3 programming layer <2023-06-05> (c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/base/article.cls +L3 programming layer <2023-05-15> (C:\Users\there\AppData\Local\Programs\MiKTeX +\tex/latex/base\article.cls Document Class: article 2022/07/02 v1.4n Standard LaTeX document class -(c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/base/size10.clo +(C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/base\size10.clo File: size10.clo 2022/07/02 v1.4n Standard LaTeX file (size option) ) \c@part=\count181 @@ -21,34 +22,38 @@ File: size10.clo 2022/07/02 v1.4n Standard LaTeX file (size option) \abovecaptionskip=\skip48 \belowcaptionskip=\skip49 \bibindent=\dimen140 -) (c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/marginnote/marginnote.sty +) +(C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/marginnote\marginnote.s +ty Package: marginnote 2018/08/09 v1.4b non floating margin notes for LaTeX \c@mn@abspage=\count189 -) (c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/graphics/graphicx.sty +) (C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/graphics\graphicx.sty Package: graphicx 2021/09/16 v1.2d Enhanced LaTeX Graphics (DPC,SPQR) -(c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/graphics/keyval.sty +(C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/graphics\keyval.sty Package: keyval 2022/05/29 v1.15 key=value parser (DPC) \KV@toks@=\toks16 -) (c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/graphics/graphics.sty +) (C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/graphics\graphics.sty Package: graphics 2022/03/10 v1.4e Standard LaTeX Graphics (DPC,SPQR) -(c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/graphics/trig.sty +(C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/graphics\trig.sty Package: trig 2021/08/11 v1.11 sin cos tan (DPC) -) (c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/graphics-cfg/graphics.cfg +) +(C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/graphics-cfg\graphics.c +fg File: graphics.cfg 2016/06/04 v1.11 sample graphics configuration ) Package graphics Info: Driver file: xetex.def on input line 107. -(c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/graphics-def/xetex.def +(C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/graphics-def\xetex.def File: xetex.def 2022/09/22 v5.0n Graphics/color driver for xetex )) \Gin@req@height=\dimen141 \Gin@req@width=\dimen142 -) (c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/xcolor/xcolor.sty +) (C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/xcolor\xcolor.sty Package: xcolor 2022/06/12 v2.14 LaTeX color extensions (UK) -(c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/graphics-cfg/color.cfg +(C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/graphics-cfg\color.cfg File: color.cfg 2016/01/02 v1.6 sample color configuration ) Package xcolor Info: Driver file: xetex.def on input line 227. -(c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/graphics/mathcolor.ltx) +(C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/graphics\mathcolor.ltx) Package xcolor Info: Model `cmy' substituted by `cmy0' on input line 1353. 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Package hyperref Info: Option `breaklinks' set `true' on input line 12. -(c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/caption/caption.sty +(C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/caption\caption.sty Package: caption 2023/03/12 v3.6j Customizing captions (AR) -(c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/caption/caption3.sty +(C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/caption\caption3.sty Package: caption3 2023/03/12 v2.4 caption3 kernel (AR) \caption@tempdima=\dimen260 \captionmargin=\dimen261 @@ -399,16 +559,19 @@ Package caption Info: Standard document class detected. \c@caption@flags=\count298 \c@continuedfloat=\count299 Package caption Info: hyperref package is loaded. -) (c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/tcolorbox/tcolorbox.sty +) +(C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/tcolorbox\tcolorbox.sty Package: tcolorbox 2023/03/17 version 6.0.3 text color boxes -(c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/tools/verbatim.sty +(C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/tools\verbatim.sty Package: verbatim 2022-07-02 v1.5u LaTeX2e package for verbatim enhancements \every@verbatim=\toks30 \verbatim@line=\toks31 \verbatim@in@stream=\read3 -) (c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/environ/environ.sty +) (C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/environ\environ.sty Package: environ 2014/05/04 v0.3 A new way to define environments -(c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/trimspaces/trimspaces.sty + +(C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/trimspaces\trimspaces.s +ty Package: trimspaces 2009/09/17 v1.1 Trim spaces around a token list ) \@envbody=\toks32 @@ -424,9 +587,9 @@ Package: trimspaces 2009/09/17 v1.1 Trim spaces around a token list \tcb@temp=\box69 \tcb@temp=\box70 \tcb@temp=\box71 -) (c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/amsfonts/amssymb.sty +) (C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/amsfonts\amssymb.sty Package: amssymb 2013/01/14 v3.01 AMS font symbols -(c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/amsfonts/amsfonts.sty +(C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/amsfonts\amsfonts.sty Package: amsfonts 2013/01/14 v3.01 Basic AMSFonts support \@emptytoks=\toks33 \symAMSa=\mathgroup4 @@ -434,20 +597,20 @@ Package: amsfonts 2013/01/14 v3.01 Basic AMSFonts support LaTeX Font Info: Redeclaring math symbol \hbar on input line 98. 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LaTeX Info: Redefining \] on input line 2954. -) (c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/generic/iftex/ifxetex.sty +) (C:\Users\there\AppData\Local\Programs\MiKTeX\tex/generic/iftex\ifxetex.sty Package: ifxetex 2019/10/25 v0.7 ifxetex legacy package. Use iftex instead. -) (c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/generic/iftex/ifluatex.sty +) (C:\Users\there\AppData\Local\Programs\MiKTeX\tex/generic/iftex\ifluatex.sty Package: ifluatex 2019/10/25 v1.5 ifluatex legacy package. 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Package biblatex Info: ... file 'blx-dm.def' found. -(c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/biblatex/blx-dm.def +(C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/biblatex\blx-dm.def File: blx-dm.def 2023/03/05 v3.19 biblatex localization (PK/MW) ) Package biblatex Info: Trying to load biblatex custom data model... @@ -670,15 +834,18 @@ Package biblatex Info: ... file 'biblatex-dm.cfg' not found. \localshorteditorwidth=\skip82 Package biblatex Info: Trying to load enhanced support for Unicode engines... Package biblatex Info: ... file 'blx-unicode.def' found. -(c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/biblatex/blx-unicode.def) + +(C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/biblatex\blx-unicode.de +f) Package biblatex Info: Trying to load compatibility code... 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Package hyperref Info: Link coloring ON on input line 295. -(./paper.out) (./paper.out) +(paper.out) (paper.out) \@outlinefile=\write6 \openout6 = `paper.out'. Package caption Info: Begin \AtBeginDocument code. Package caption Info: longtable package is loaded. -(c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/caption/ltcaption.sty +(C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/caption\ltcaption.sty Package: ltcaption 2021/01/08 v1.4c longtable captions (AR) ) Package caption Info: End \AtBeginDocument code. Package biblatex Info: Trying to load language 'english'... Package biblatex Info: ... file 'english.lbx' found. -(c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/biblatex/lbx/english.lbx + +(C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/biblatex/lbx\english.lb +x File: english.lbx 2023/03/05 v3.19 biblatex localization (PK/MW) ) Package biblatex Info: XeTeX detected. @@ -1007,8 +1213,11 @@ Package microtype Info: Using protrusion set `basicmath'. Package microtype Info: No adjustment of tracking. Package microtype Info: No adjustment of spacing. 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[2] LaTeX Font Info: Font shape `TU/lmtt/bx/n' in size <10> not available -(Font) Font shape `TU/lmtt/b/n' tried instead on input line 449. +(Font) Font shape `TU/lmtt/b/n' tried instead on input line 458. -Overfull \hbox (32.66139pt too wide) in paragraph at lines 465--465 -[]\TU/lmtt/m/n/10 #> -----------------------------------------------------------------------------[] +Overfull \hbox (32.66139pt too wide) in paragraph at lines 474--474 +[]\TU/lmtt/m/n/10 #> ---------------------------------------------------------- +-------------------[] [] -Overfull \hbox (32.66139pt too wide) in paragraph at lines 474--474 -[]\TU/lmtt/m/n/10 #> -----------------------------------------------------------------------------[] +Overfull \hbox (32.66139pt too wide) in paragraph at lines 483--483 +[]\TU/lmtt/m/n/10 #> ---------------------------------------------------------- +-------------------[] [] -File: D:/Rpackages/rticles/rmarkdown/templates/joss/resources/JOSE-logo.png Graphic file (type bmp) - +File: C:/Users/there/AppData/Local/R/win-library/4.3/rticles/rmarkdown/template +s/joss/resources/JOSE-logo.png Graphic file (type bmp) + Package fancyhdr Warning: \headheight is too small (62.59596pt): (fancyhdr) Make it at least 64.31554pt, for example: (fancyhdr) \setlength{\headheight}{64.31554pt}. (fancyhdr) You might also make \topmargin smaller to compensate: + (fancyhdr) \addtolength{\topmargin}{-1.71957pt}. [3] -File: D:/Rpackages/rticles/rmarkdown/templates/joss/resources/JOSE-logo.png Graphic file (type bmp) - +File: C:/Users/there/AppData/Local/R/win-library/4.3/rticles/rmarkdown/template +s/joss/resources/JOSE-logo.png Graphic file (type bmp) + Package fancyhdr Warning: \headheight is too small (62.59596pt): (fancyhdr) Make it at least 64.31554pt, for example: (fancyhdr) \setlength{\headheight}{64.31554pt}. (fancyhdr) You might also make \topmargin smaller to compensate: + (fancyhdr) \addtolength{\topmargin}{-1.71957pt}. [4] File: paper_files/figure-latex/model-1.pdf Graphic file (type pdf) -File: D:/Rpackages/rticles/rmarkdown/templates/joss/resources/JOSE-logo.png Graphic file (type bmp) - +File: C:/Users/there/AppData/Local/R/win-library/4.3/rticles/rmarkdown/template +s/joss/resources/JOSE-logo.png Graphic file (type bmp) + Package fancyhdr Warning: \headheight is too small (62.59596pt): (fancyhdr) Make it at least 64.31554pt, for example: (fancyhdr) \setlength{\headheight}{64.31554pt}. (fancyhdr) You might also make \topmargin smaller to compensate: + (fancyhdr) \addtolength{\topmargin}{-1.71957pt}. [5] -File: D:/Rpackages/rticles/rmarkdown/templates/joss/resources/JOSE-logo.png Graphic file (type bmp) - +File: C:/Users/there/AppData/Local/R/win-library/4.3/rticles/rmarkdown/template +s/joss/resources/JOSE-logo.png Graphic file (type bmp) + Package fancyhdr Warning: \headheight is too small (62.59596pt): (fancyhdr) Make it at least 64.31554pt, for example: (fancyhdr) \setlength{\headheight}{64.31554pt}. (fancyhdr) You might also make \topmargin smaller to compensate: + (fancyhdr) \addtolength{\topmargin}{-1.71957pt}. [6] -File: D:/Rpackages/rticles/rmarkdown/templates/joss/resources/JOSE-logo.png Graphic file (type bmp) - +File: C:/Users/there/AppData/Local/R/win-library/4.3/rticles/rmarkdown/template +s/joss/resources/JOSE-logo.png Graphic file (type bmp) + Package fancyhdr Warning: \headheight is too small (62.59596pt): (fancyhdr) Make it at least 64.31554pt, for example: (fancyhdr) \setlength{\headheight}{64.31554pt}. (fancyhdr) You might also make \topmargin smaller to compensate: + (fancyhdr) \addtolength{\topmargin}{-1.71957pt}. [7] -Underfull \hbox (badness 1584) in paragraph at lines 910--916 -[]\TU/lmr/m/n/10 Simmons, J. P., Nelson, L. D., & Simonsohn, U. (2011). False-positive psy- +Underfull \hbox (badness 1584) in paragraph at lines 919--925 +[]\TU/lmr/m/n/10 Simmons, J. P., Nelson, L. D., & Simonsohn, U. (2011). False-p +ositive psy- [] -Underfull \hbox (badness 3049) in paragraph at lines 910--916 -\TU/lmr/m/n/10 chology: Undisclosed flexibility in data collection and analysis allows pre- +Underfull \hbox (badness 3049) in paragraph at lines 919--925 +\TU/lmr/m/n/10 chology: Undisclosed flexibility in data collection and analysis + allows pre- [] -Underfull \hbox (badness 3735) in paragraph at lines 910--916 -\TU/lmr/m/n/10 senting anything as significant. \TU/lmr/m/it/10 Psychological Science\TU/lmr/m/n/10 , \TU/lmr/m/it/10 22\TU/lmr/m/n/10 (11), 1359–1366. +Underfull \hbox (badness 3735) in paragraph at lines 919--925 +\TU/lmr/m/n/10 senting anything as significant. \TU/lmr/m/it/10 Psychological S +cience\TU/lmr/m/n/10 , \TU/lmr/m/it/10 22\TU/lmr/m/n/10 (11), 1359–1366. [] -File: D:/Rpackages/rticles/rmarkdown/templates/joss/resources/JOSE-logo.png Graphic file (type bmp) - +File: C:/Users/there/AppData/Local/R/win-library/4.3/rticles/rmarkdown/template +s/joss/resources/JOSE-logo.png Graphic file (type bmp) + Package fancyhdr Warning: \headheight is too small (62.59596pt): (fancyhdr) Make it at least 64.31554pt, for example: (fancyhdr) \setlength{\headheight}{64.31554pt}. (fancyhdr) You might also make \topmargin smaller to compensate: + (fancyhdr) \addtolength{\topmargin}{-1.71957pt}. -[8] (./paper.aux) +[8] (paper.aux) Package rerunfilecheck Info: File `paper.out' has not changed. (rerunfilecheck) Checksum: EEBE57815200557F8EDD73A1BF6F9118;2043. Package logreq Info: Writing requests to 'paper.run.xml'. @@ -1159,12 +1403,12 @@ Package logreq Info: Writing requests to 'paper.run.xml'. ) Here is how much of TeX's memory you used: - 37274 strings out of 478641 - 768952 string characters out of 5846292 - 1872382 words of memory out of 5000000 - 56849 multiletter control sequences out of 15000+600000 - 520299 words of font info for 87 fonts, out of 8000000 for 9000 - 14 hyphenation exceptions out of 8191 - 84i,12n,81p,1194b,848s stack positions out of 10000i,1000n,20000p,200000b,200000s + 37316 strings out of 411547 + 752904 string characters out of 5819451 + 1873476 words of memory out of 5000000 + 56952 multiletter control sequences out of 15000+600000 + 519199 words of font info for 85 fonts, out of 8000000 for 9000 + 1348 hyphenation exceptions out of 8191 + 84i,12n,81p,1196b,850s stack positions out of 10000i,1000n,20000p,200000b,200000s Output written on paper.pdf (8 pages). diff --git a/papers/JOSE/paper.md b/papers/JOSE/paper.md index b6c3946b9..983f9824d 100644 --- a/papers/JOSE/paper.md +++ b/papers/JOSE/paper.md @@ -99,10 +99,11 @@ Beyond the challenge of keeping up-to-date with current best practices regarding Real-life data often contain observations that can be considered *abnormal* when compared to the main population. The cause of it---be it because they belong to a different distribution (originating from a different generative process) or simply being extreme cases, statistically rare but not impossible---can be hard to assess, and the boundaries of "abnormal" difficult to define. -Nonetheless, the improper handling of these outliers can substantially affect statistical model estimations, biasing effect estimations and weakening the models' predictive performance. -It is thus essential to address this problem in a thoughtful manner. Yet, despite the existence of established recommendations and guidelines, many researchers still do not treat outliers in a consistent manner, or do so using inappropriate strategies [@simmons2011false; @leys2013outliers]. +Nonetheless, the improper handling of these outliers can substantially affect statistical model estimations, biasing effect estimations and weakening the models' predictive performance. It is thus essential to address this problem in a thoughtful manner. Yet, despite the existence of established recommendations and guidelines, many researchers still do not treat outliers in a consistent manner, or do so using inappropriate strategies [@simmons2011false; @leys2013outliers]. -One possible reason is that researchers are not aware of the existing recommendations, or do not know how to implement them using their analysis software. In this paper, we show how to follow current best practices for automatic and reproducible statistical outlier detection (SOD) using R and the *{performance}* package [@ludecke2021performance], which is part of the *easystats* ecosystem of packages that build an R framework for easy statistical modeling, visualization, and reporting [@easystatspackage]. +One possible reason is that researchers are not aware of the existing recommendations, or do not know how to implement them using their analysis software. In this paper, we show how to follow current best practices for automatic and reproducible statistical outlier detection (SOD) using R and the *{performance}* package [@ludecke2021performance], which is part of the *easystats* ecosystem of packages that build an R framework for easy statistical modeling, visualization, and reporting [@easystatspackage]. Installation instructions can be found on [GitHub](https://github.com/easystats/performance) or its [website](https://easystats.github.io/performance/), and its list of dependencies on [CRAN](https://cran.r-project.org/package=performance). + +The instructional materials that follow is aimed at an audience of researchers who want to follow good practices, and is appropriate for advanced undergraduate students, graduate students, professors, or professionals having to deal with the nuances of outlier treatment. # Identifying Outliers diff --git a/papers/JOSE/paper.pdf b/papers/JOSE/paper.pdf index f3c3372a63f712d83bb9868f375a624fe19b01a2..76bf20f3be338d90a945ebc5d52f26f571724f2e 100644 GIT binary patch delta 20413 zcmZ5{V|Zpu({7$*Voq#(Vw)4&w#|u?C$??dwlT5oiEaDLe)o6qo*(P#rLOL-uDVxg zg@?m^y}tJRYd$W-x@zP56w~R@iGlhDDu;(bsN%!m>+ev@x#5Ps9Cqd#2rn6zWh$3*VhW#M*{yz@IiBkuM+wL$v> zv&+fj*PrZA@~0PjI-x6V`^meg&hSa6JdPHvt<};Kn$^7LaZA-{UB=m=7BfuXTlvQc 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zE95L(4hF?>vLUc=Ik+qsdisD}!GPZjsEo|%gyA1NSy`!n@#JJq!uWo#;Oupy;^X z!+>EYLH;H*z~+kT(lSyS>Tnr2LS0T%7A|vD2CgM5BMXIHgQ}||WVDpQ|3AbMd~)WV ZUbY@yJ{}JD04MVmDS)7$rhyhE;6Hm>chdj> From eb41cd2cd8027ca64747a8a34e9c233fbce80bb8 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?R=C3=A9mi=20Th=C3=A9riault?= <13123390+rempsyc@users.noreply.github.com> Date: Wed, 27 Sep 2023 19:54:20 -0400 Subject: [PATCH 21/34] add check_outliers vignette --- vignettes/check_outliers.Rmd | 267 +++++++++++++++++++++++++++++++++++ vignettes/paper.bib | 161 +++++++++++++++++++++ 2 files changed, 428 insertions(+) create mode 100644 vignettes/check_outliers.Rmd create mode 100644 vignettes/paper.bib diff --git a/vignettes/check_outliers.Rmd b/vignettes/check_outliers.Rmd new file mode 100644 index 000000000..804be2432 --- /dev/null +++ b/vignettes/check_outliers.Rmd @@ -0,0 +1,267 @@ +--- +title: "Checking outliers with *performance*" +output: + rmarkdown::html_vignette: + toc: true + fig_width: 10.08 + fig_height: 6 +bibliography: paper.bib +vignette: > + \usepackage[utf8]{inputenc} + %\VignetteIndexEntry{Checking model assumption - linear models} + %\VignetteEngine{knitr::rmarkdown} +editor_options: + chunk_output_type: console +--- + +```{r , include=FALSE} +library(knitr) +library(performance) +options(knitr.kable.NA = "") +knitr::opts_chunk$set( + comment = ">", + message = FALSE, + warning = FALSE, + out.width = "100%", + dpi = 450 +) +options(digits = 2) + +pkgs <- c("see", "performance", "datawizard", "rempsyc") +successfully_loaded <- vapply(pkgs, requireNamespace, FUN.VALUE = logical(1L), quietly = TRUE) +can_evaluate <- all(successfully_loaded) + +if (can_evaluate) { + knitr::opts_chunk$set(eval = TRUE) + vapply(pkgs, require, FUN.VALUE = logical(1L), quietly = TRUE, character.only = TRUE) +} else { + knitr::opts_chunk$set(eval = FALSE) +} +``` + + +# Reuse of this Material + +> Note: This vignette is an extended write-up of the [JOSE paper](https://jose.theoj.org/papers/42749638170253bb2854649fb52bf4ca). This educational module can be freely reused for teaching purposes as long as the original JOSE paper and this vignette are cited or acknowledged. The raw code file, which can be adapted to other rmarkdown formats for teaching purposes, can be accessed [here](https://github.com/easystats/performance/blob/HEAD/vignettes/check_outliers.Rmd). To contribute to and improve this content directly, please submit a Pull Request at the *{performance}* package GitHub repository by following our usual contributing guidelines: https://easystats.github.io/performance/CONTRIBUTING.html. To report issues or problems, with this module, or seek support, please open an issue: https://github.com/easystats/performance/issues. + +# Summary + +Beyond the challenge of keeping up-to-date with current best practices regarding the diagnosis and treatment of outliers, an additional difficulty arises concerning the mathematical implementation of the recommended methods. In this paper, we provide an overview of current recommendations and best practices and demonstrate how they can easily and conveniently be implemented in the R statistical computing software, using the *{performance}* package of the *easystats* ecosystem. We cover univariate, multivariate, and model-based statistical outlier detection methods, their recommended threshold, standard output, and plotting methods. We conclude with recommendations on the handling of outliers: the different theoretical types of outliers, whether to exclude or winsorize them, and the importance of transparency. + +# Statement of Need + +Real-life data often contain observations that can be considered *abnormal* when compared to the main population. The cause of it---be it because they belong to a different distribution (originating from a different generative process) or simply being extreme cases, statistically rare but not impossible---can be hard to assess, and the boundaries of "abnormal" difficult to define. + +Nonetheless, the improper handling of these outliers can substantially affect statistical model estimations, biasing effect estimations and weakening the models' predictive performance. It is thus essential to address this problem in a thoughtful manner. Yet, despite the existence of established recommendations and guidelines, many researchers still do not treat outliers in a consistent manner, or do so using inappropriate strategies [@simmons2011false; @leys2013outliers]. + +One possible reason is that researchers are not aware of the existing recommendations, or do not know how to implement them using their analysis software. In this paper, we show how to follow current best practices for automatic and reproducible statistical outlier detection (SOD) using R and the *{performance}* package [@ludecke2021performance], which is part of the *easystats* ecosystem of packages that build an R framework for easy statistical modeling, visualization, and reporting [@easystatspackage]. Installation instructions can be found on [GitHub](https://github.com/easystats/performance) or its [website](https://easystats.github.io/performance/), and its list of dependencies on [CRAN](https://cran.r-project.org/package=performance). + +The instructional materials that follow is aimed at an audience of researchers who want to follow good practices, and is appropriate for advanced undergraduate students, graduate students, professors, or professionals having to deal with the nuances of outlier treatment. + +# Identifying Outliers + +Although many researchers attempt to identify outliers with measures based on the mean (e.g., _z_ scores), those methods are problematic because the mean and standard deviation themselves are not robust to the influence of outliers and they assume normally distributed data (i.e., a Gaussian distribution). Therefore, current guidelines recommend using robust methods to identify outliers, such as those relying on the median as opposed to the mean [@leys2019outliers; @leys2013outliers; @leys2018outliers]. + +Nonetheless, which exact outlier method to use depends on many factors. In some cases, eye-gauging odd observations can be an appropriate solution, though many researchers will favour algorithmic solutions to detect potential outliers, for example, based on a continuous value expressing the observation stands out from the others. + +One of the factors to consider when selecting an algorithmic outlier detection method is the statistical test of interest. When using a regression model, relevant information can be found by identifying observations that do not fit well with the model. This approach, known as model-based outliers detection (as outliers are extracted after the statistical model has been fit), can be contrasted with distribution-based outliers detection, which is based on the distance between an observation and the "center" of its population. Various quantification strategies of this distance exist for the latter, both univariate (involving only one variable at a time) or multivariate (involving multiple variables). + +When no method is readily available to detect model-based outliers, such as for structural equation modelling (SEM), looking for multivariate outliers may be of relevance. For simple tests (_t_ tests or correlations) that compare values of the same variable, it can be appropriate to check for univariate outliers. However, univariate methods can give false positives since _t_ tests and correlations, ultimately, are also models/multivariable statistics. They are in this sense more limited, but we show them nonetheless for educational purposes. + +Importantly, whatever approach researchers choose remains a subjective decision, which usage (and rationale) must be transparently documented and reproducible [@leys2019outliers]. Researchers should commit (ideally in a preregistration) to an outlier treatment method before collecting the data. They should report in the paper their decisions and details of their methods, as well as any deviation from their original plan. These transparency practices can help reduce false positives due to excessive researchers' degrees of freedom (i.e., choice flexibility throughout the analysis). In the following section, we will go through each of the mentioned methods and provide examples on how to implement them with R. + +## Univariate Outliers + +Researchers frequently attempt to identify outliers using measures of deviation from the center of a variable's distribution. One of the most popular such procedure is the _z_ score transformation, which computes the distance in standard deviation (SD) from the mean. However, as mentioned earlier, this popular method is not robust. Therefore, for univariate outliers, it is recommended to use the median along with the Median Absolute Deviation (MAD), which are more robust than the interquartile range or the mean and its standard deviation [@leys2019outliers; @leys2013outliers]. + +Researchers can identify outliers based on robust (i.e., MAD-based) _z_ scores using the `check_outliers()` function of the *{performance}* package, by specifying `method = "zscore_robust"`.^[Note that `check_outliers()` only checks numeric variables.] Although @leys2013outliers suggest a default threshold of 2.5 and @leys2019outliers a threshold of 3, *{performance}* uses by default a less conservative threshold of ~3.29.^[3.29 is an approximation of the two-tailed critical value for _p_ < .001, obtained through `qnorm(p = 1 - 0.001 / 2)`. We chose this threshold for consistency with the thresholds of all our other methods.] That is, data points will be flagged as outliers if they go beyond +/- ~3.29 MAD. Users can adjust this threshold using the `threshold` argument, as demonstrated below. + +```{r z_score} +library(performance) + +# Create some artificial outliers and an ID column +data <- rbind(mtcars[1:4], 42, 55) +data <- cbind(car = row.names(data), data) + +outliers <- check_outliers(data, method = "zscore_robust", ID = "car") +outliers +``` + +The row numbers of the detected outliers can be obtained by using `which()` on the output object, which can be used for exclusions for example: + +```{r} +which(outliers) + +data_clean <- data[-which(outliers), ] +``` + +All `check_outliers()` output objects possess a `plot()` method, meaning it is also possible to visualize the outliers using the generic `plot()` function on the resulting outlier object after loading the {see} package. + +```{r univariate, eval=FALSE} +library(see) +plot(outliers) +``` + +```{r univariate_implicit, fig.cap = "Visual depiction of outliers using the robust z-score method. The distance represents an aggregate score for variables mpg, cyl, disp, and hp.", echo=FALSE} +library(see) +plot(outliers) + + ggplot2::theme(axis.text.x = ggplot2::element_text( + angle = 45, size = 7 +)) +``` + +Other univariate methods are available, such as using the interquartile range (IQR), or based on different intervals, such as the Highest Density Interval (HDI) or the Bias Corrected and Accelerated Interval (BCI). These methods are documented and described in the function's [help page](). + +## Multivariate Outliers + +Univariate outliers can be useful when the focus is on a particular variable, for instance the reaction time, as extreme values might be indicative of inattention or non-task-related behavior^[ Note that they might not be the optimal way of treating reaction time outliers [@ratcliff1993methods; @van1995statistical]]. + +However, in many scenarios, variables of a data set are not independent, and an abnormal observation will impact multiple dimensions. For instance, a participant giving random answers to a questionnaire. In this case, computing the _z_ score for each of the questions might not lead to satisfactory results. Instead, one might want to look at these variables together. + +One common approach for this is to compute multivariate distance metrics such as the Mahalanobis distance. Although the Mahalanobis distance is very popular, just like the regular _z_ scores method, it is not robust and is heavily influenced by the outliers themselves. Therefore, for multivariate outliers, it is recommended to use the Minimum Covariance Determinant, a robust version of the Mahalanobis distance [MCD, @leys2018outliers; @leys2019outliers]. + +In *{performance}*'s `check_outliers()`, one can use this approach with `method = "mcd"`.^[Our default threshold for the MCD method is defined by `stats::qchisq(p = 1 - 0.001, df = ncol(x))`, which again is an approximation of the critical value for _p_ < .001 consistent with the thresholds of our other methods.] + +```{r multivariate} +outliers <- check_outliers(data, method = "mcd") +outliers +``` + +```{r multivariate_plot, eval=FALSE} +plot(outliers) +``` + +```{r multivariate_implicit, fig.cap = "Visual depiction of outliers using the Minimum Covariance Determinant (MCD) method, a robust version of the Mahalanobis distance. The distance represents the MCD scores for variables mpg, cyl, disp, and hp.", echo=FALSE} +plot(outliers) + + ggplot2::theme(axis.text.x = ggplot2::element_text( + angle = 45, size = 7 +)) +``` + +Other multivariate methods are available, such as another type of robust Mahalanobis distance that in this case relies on an orthogonalized Gnanadesikan-Kettenring pairwise estimator [@gnanadesikan1972robust]. These methods are documented and described in the function's [help page](https://easystats.github.io/performance/reference/check_outliers.html). + +## Model-Based Outliers + +Working with regression models creates the possibility of using model-based SOD methods. These methods rely on the concept of *leverage*, that is, how much influence a given observation can have on the model estimates. If few observations have a relatively strong leverage/influence on the model, one can suspect that the model's estimates are biased by these observations, in which case flagging them as outliers could prove helpful (see next section, "Handling Outliers"). + +In {performance}, two such model-based SOD methods are currently available: Cook's distance, for regular regression models, and Pareto, for Bayesian models. As such, `check_outliers()` can be applied directly on regression model objects, by simply specifying `method = "cook"` (or `method = "pareto"` for Bayesian models).^[Our default threshold for the Cook method is defined by `stats::qf(0.5, ncol(x), nrow(x) - ncol(x))`, which again is an approximation of the critical value for _p_ < .001 consistent with the thresholds of our other methods.] + +```{r model, fig.cap = "Visual depiction of outliers based on Cook's distance (leverage and standardized residuals), based on the fitted model."} +model <- lm(disp ~ mpg * disp, data = data) +outliers <- check_outliers(model, method = "cook") +outliers + +plot(outliers) +``` + +Table 1 below summarizes which methods to use in which cases, and with what threshold. + +```{r, echo=FALSE} +df <- data.frame( + `Statistical Test` = c( + "Supported regression model", + "Structural Equation Modeling (or other unsupported model)", + "Simple test with few variables (*t* test, correlation, etc.)"), + `Diagnosis Method` = c( + "**Model-based**: Cook (or Pareto for Bayesian models)", + "**Multivariate**: Minimum Covariance Determinant (MCD)", + "**Univariate**: robust *z* scores (MAD)"), + `Recommended Threshold` = c( + "`qf(0.5, ncol(x), nrow(x) - ncol(x))` (or 0.7 for Pareto)", + "`qchisq(p = 1 - 0.001, df = ncol(x))`", + "`qnorm(p = 1 - 0.001 / 2)`, ~ 3.29") +) +knitr::kable( + df, col.names = gsub("[.]", " ", names(df)), + caption = "Summary of Statistical Outlier Detection Methods Recommendations.", longtable = TRUE) +``` + +## Cook's Distance vs. MCD + +@leys2018outliers report a preference for the MCD method over Cook's distance. This is because Cook's distance removes one observation at a time and checks its corresponding influence on the model each time [@cook1977detection], and flags any observation that has a large influence. In the view of these authors, when there are several outliers, the process of removing a single outlier at a time is problematic as the model remains "contaminated" or influenced by other possible outliers in the model, rendering this method suboptimal in the presence of multiple outliers. + +However, distribution-based approaches are not a silver bullet either, and there are cases where the usage of methods agnostic to theoretical and statistical models of interest might be problematic. For example, a very tall person would be expected to also be much heavier than average, but that would still fit with the expected association between height and weight (i.e., it would be in line with a model such as `weight ~ height`). In contrast, using multivariate outlier detection methods there may flag this person as being an outlier---being unusual on two variables, height and weight---even though the pattern fits perfectly with our predictions. + +In the example below, we plot the raw data and see two possible outliers. The first one falls along the regression line, and is therefore "in line" with our hypothesis. The second one clearly diverges from the regression line, and therefore we can conclude that this outlier may have a disproportionate influence on our model. + +```{r scatter, fig.cap = "Scatter plot of height and weight, with two extreme observations: one model-consistent (top-right) and the other, model-inconsistent (i.e., an outlier; bottom-right)."} +data <- women[rep(seq_len(nrow(women)), each = 100), ] +data <- rbind(data, c(100, 258), c(100, 200)) +model <- lm(weight ~ height, data) +rempsyc::nice_scatter(data, "height", "weight") +``` + +Using either the *z*-score or MCD methods, our model-consistent observation will be incorrectly flagged as an outlier or influential observation. + +```{r} +outliers <- check_outliers(model, method = c("zscore_robust", "mcd")) +which(outliers) +``` + +In contrast, the model-based detection method displays the desired behaviour: it correctly flags the person who is very tall but very light, without flagging the person who is both tall and heavy. + +```{r model2, fig.cap = "The leverage method (Cook's distance) correctly distinguishes the true outlier from the model-consistent extreme observation), based on the fitted model."} +outliers <- check_outliers(model, method = "cook") +which(outliers) +plot(outliers) +``` + +Finally, unusual observations happen naturally: extreme observations are expected even when taken from a normal distribution. While statistical models can integrate this "expectation", multivariate outlier methods might be too conservative, flagging too many observations despite belonging to the right generative process. For these reasons, we believe that model-based methods are still preferable to the MCD when using supported regression models. Additionally, if the presence of multiple outliers is a significant concern, regression methods that are more robust to outliers should be considered---like _t_ regression or quantile regression---as they render their precise identification less critical [@mcelreath2020statistical]. + +## Composite Outlier Score + +The *{performance}* package also offers an alternative, consensus-based approach that combines several methods, based on the assumption that different methods provide different angles of looking at a given problem. By applying a variety of methods, one can hope to "triangulate" the true outliers (those consistently flagged by multiple methods) and thus attempt to minimize false positives. + +In practice, this approach computes a composite outlier score, formed of the average of the binary (0 or 1) classification results of each method. It represents the probability that each observation is classified as an outlier by at least one method. The default decision rule classifies rows with composite outlier scores superior or equal to 0.5 as outlier observations (i.e., that were classified as outliers by at least half of the methods). In *{performance}*'s `check_outliers()`, one can use this approach by including all desired methods in the corresponding argument. + +```{r multimethod, fig.cap = "Visual depiction of outliers using several different statistical outlier detection methods."} +outliers <- check_outliers(model, method = c("zscore_robust", "mcd", "cook")) +which(outliers) +``` + +Outliers (counts or per variables) for individual methods can then be obtained through attributes. For example: + +```{r} +attributes(outliers)$outlier_var$zscore_robust +``` + +An example sentence for reporting the usage of the composite method could be: + +> Based on a composite outlier score [see the 'check_outliers()' function in the 'performance' R package, @ludecke2021performance] obtained via the joint application of multiple outliers detection algorithms [(a) median absolute deviation (MAD)-based robust _z_ scores, @leys2013outliers; (b) Mahalanobis minimum covariance determinant (MCD), @leys2019outliers; and (c) Cook's distance, @cook1977detection], we excluded two participants that were classified as outliers by at least half of the methods used. + +# Handling Outliers + +The above section demonstrated how to identify outliers using the `check_outliers()` function in the *{performance}* package. But what should we do with these outliers once identified? Although it is common to automatically discard any observation that has been marked as "an outlier" as if it might infect the rest of the data with its statistical ailment, we believe that the use of SOD methods is but one step in the get-to-know-your-data pipeline; a researcher or analyst's _domain knowledge_ must be involved in the decision of how to deal with observations marked as outliers by means of SOD. Indeed, automatic tools can help detect outliers, but they are nowhere near perfect. Although they can be useful to flag suspect data, they can have misses and false alarms, and they cannot replace human eyes and proper vigilance from the researcher. If you do end up manually inspecting your data for outliers, it can be helpful to think of outliers as belonging to different types of outliers, or categories, which can help decide what to do with a given outlier. + +## Error, Interesting, and Random Outliers + +@leys2019outliers distinguish between error outliers, interesting outliers, and random outliers. _Error outliers_ are likely due to human error and should be corrected before data analysis or outright removed since they are invalid observations. _Interesting outliers_ are not due to technical error and may be of theoretical interest; it might thus be relevant to investigate them further even though they should be removed from the current analysis of interest. _Random outliers_ are assumed to be due to chance alone and to belong to the correct distribution and, therefore, should be retained. + +It is recommended to _keep_ observations which are expected to be part of the distribution of interest, even if they are outliers [@leys2019outliers]. However, if it is suspected that the outliers belong to an alternative distribution, then those observations could have a large impact on the results and call into question their robustness, especially if significance is conditional on their inclusion, so should be removed. + +On the other hand, there are also outliers that cannot be detected by statistical tools, but should be found and removed. For example, if we are studying the effects of X on Y among teenagers and we have one observation from a 20-year-old, this observation might not be a _statistical outlier_, but it is an outlier in the _context_ of our research, and should be discarded to allow for valid inferences. + +## Winsorization + +_Removing_ outliers can in this case be a valid strategy, and ideally one would report results with and without outliers to see the extent of their impact on results. This approach however can reduce statistical power. Therefore, some propose a _recoding_ approach, namely, winsorization: bringing outliers back within acceptable limits [e.g., 3 MADs, @tukey1963less]. However, if possible, it is recommended to collect enough data so that even after removing outliers, there is still sufficient statistical power without having to resort to winsorization [@leys2019outliers]. + +The _easystats_ ecosystem makes it easy to incorporate this step into your workflow through the `winsorize()` function of *{datawizard}*, a lightweight R package to facilitate data wrangling and statistical transformations [@patil2022datawizard]. This procedure will bring back univariate outliers within the limits of 'acceptable' values, based either on the percentile, the _z_ score, or its robust alternative based on the MAD. + +```{r winsorization} +data[1501:1502, ] # See outliers rows +# Winsorizing using the MAD +library(datawizard) +winsorized_data <- winsorize(data, method = "zscore", robust = TRUE, threshold = 3) +# Values > +/- MAD have been winsorized +winsorized_data[1501:1502, ] +``` + +## The Importance of Transparency + +Once again, it is a critical part of a sound outlier treatment that regardless of which SOD method used, it should be reported in a reproducible manner. Ideally, the handling of outliers should be specified *a priori* with as much detail as possible, and preregistered, to limit researchers' degrees of freedom and therefore risks of false positives [@leys2019outliers]. This is especially true given that interesting outliers and random outliers are often times hard to distinguish in practice. Thus, researchers should always prioritize transparency and report all of the following information: (a) how many outliers were identified (including percentage); (b) according to which method and criteria, (c) using which function of which R package (if applicable), and (d) how they were handled (excluded or winsorized, if the latter, using what threshold). If at all possible, (e) the corresponding code script along with the data should be shared on a public repository like the Open Science Framework (OSF), so that the exclusion criteria can be reproduced precisely. + +# Conclusion + +In this vignette, we have showed how to investigate outliers using the `check_outliers()` function of the *{performance}* package while following current good practices. However, best practice for outlier treatment does not stop at using appropriate statistical algorithms, but entails respecting existing recommendations, such as preregistration, reproducibility, consistency, transparency, and justification. Ideally, one would additionally also report the package, function, and threshold used (linking to the full code when possible). We hope that this paper and the accompanying `check_outlier()` function of *easystats* will help researchers engage in good research practices while providing a smooth outlier detection experience. + +# References diff --git a/vignettes/paper.bib b/vignettes/paper.bib new file mode 100644 index 000000000..56c8ae7e1 --- /dev/null +++ b/vignettes/paper.bib @@ -0,0 +1,161 @@ +@article{leys2019outliers, + title = {How to Classify, Detect, and Manage Univariate and Multivariate Outliers, With Emphasis on Pre-Registration},author = {Leys, Christophe and Delacre, Marie and Mora, Youri L. and Lakens, Daniël and Ley, Christophe}, + journal = {International Review of Social Psychology}, + year = {2019}, + doi = {10.5334/irsp.289} +} + +@article{leys2013outliers, + title = {Detecting outliers: Do not use standard deviation around the mean, use absolute deviation around the median}, + author = {Christophe Leys and Christophe Ley and Olivier Klein and Philippe Bernard and Laurent Licata}, + journal = {Journal of Experimental Social Psychology}, + volume = {49}, + number = {4}, + pages = {764-766}, + year = {2013}, + doi = {10.1016/j.jesp.2013.03.013}, + url = {https://doi.org/10.1016/j.jesp.2013.03.013} +} + +@article{leys2018outliers, + title = {Detecting multivariate outliers: Use a robust variant of the Mahalanobis distance}, + journal = {Journal of Experimental Social Psychology}, + volume = {74}, + pages = {150-156}, + year = {2018}, + issn = {0022-1031}, + doi = {10.1016/j.jesp.2017.09.011}, + url = {https://www.sciencedirect.com/science/article/pii/S0022103117302123}, + author = {Christophe Leys and Olivier Klein and Yves Dominicy and Christophe Ley}, +} + +@article{simmons2011false, + author = {Joseph P. Simmons and Leif D. Nelson and Uri Simonsohn}, + title ={False-Positive Psychology: Undisclosed Flexibility in Data Collection and Analysis Allows Presenting Anything as Significant}, + journal = {Psychological Science}, + volume = {22}, + number = {11}, + pages = {1359-1366}, + year = {2011}, + doi = {10.1177/0956797611417632}, + URL = {https://doi.org/10.1177/0956797611417632}, +} + +@software{easystatspackage, + title = {{easystats}: Streamline Model Interpretation, Visualization, and Reporting}, + author = {Daniel Lüdecke and Dominique Makowski and Mattan S. Ben-Shachar and Indrajeet Patil and Brenton M. Wiernik and Etienne Bacher and Rémi Thériault}, + date = {2023-02-04T22:06:06Z}, + origdate = {2019-01-28T10:39:29Z}, + url = {https://easystats.github.io/easystats/} +} + +@Article{ludecke2021performance, + author = {Daniel Lüdecke and Mattan S. Ben-Shachar and Indrajeet Patil and Philip Waggoner and Dominique Makowski}, + title = {{performance}: An {R} package for assessment, comparison and testing of statistical models}, + volume = {6}, + number = {60}, + journal = {Journal of Open Source Software}, + year = {2021}, + pages = {3139}, + doi = {10.21105/joss.03139}, + url = {https://doi.org/10.21105/joss.03139} + } + +@Article{patil2022datawizard, + title = {{datawizard}: An {R} package for easy data preparation and statistical transformations}, + author = {Indrajeet Patil and Dominique Makowski and Mattan S. Ben-Shachar and Brenton M. Wiernik and Etienne Bacher and Daniel Lüdecke}, + journal = {Journal of Open Source Software}, + year = {2022}, + volume = {7}, + number = {78}, + pages = {4684}, + doi = {10.21105/joss.04684}, + } + +@article{cook1977detection, + author = {R. Dennis Cook}, + title = {Detection of Influential Observation in Linear Regression}, + journal = {Technometrics}, + volume = {19}, + number = {1}, + pages = {15-18}, + year = {1977}, + publisher = {Taylor & Francis}, + doi = {10.1080/00401706.1977.10489493} +} + +@book{iglewicz1993outliers, + title = {How to detect and handle outliers (Vol. 16)}, + publisher = {Asq Press}, + author = {Iglewicz, B. and Hoaglin, D. C}, + year = {1993} +} + +@article{gnanadesikan1972robust, + title = {Robust estimates, residuals, and outlier detection with multiresponse data}, + author = {Gnanadesikan, R. and Kettenring, J. R}, + journal = {Biometrics}, + pages = {81-124}, + year = {1972} +} + +@article{hubert2018mcd, + author = {Hubert, Mia and Debruyne, Michiel and Rousseeuw, Peter J.}, + title = {Minimum covariance determinant and extensions}, + journal = {Wiley Interdisciplinary Reviews: Computational Statistics}, + volume = {10}, + number = {3}, + pages = {e1421}, + doi = {10.1002/wics.1421}, + url = {https://doi.org/10.1002/wics.1421}, + year = {2018} +} + +@article{tukey1963less, + title={Less vulnerable confidence and significance procedures for location based on a single sample: Trimming/Winsorization 1}, + author={Tukey, John W and McLaughlin, Donald H}, + journal={Sankhy{\=a}: The Indian Journal of Statistics, Series A}, + pages={331--352}, + year={1963}, + publisher={JSTOR} +} + +@article{van1995statistical, + title={Statistical mimicking of reaction time data: Single-process models, parameter variability, and mixtures}, + author={Van Zandt, Trisha and Ratcliff, Roger}, + journal={Psychonomic Bulletin \& Review}, + volume={2}, + number={1}, + pages={20--54}, + year={1995}, + publisher={Springer}, + doi = {10.3758/BF03214411} +} + +@article{ratcliff1993methods, + title={Methods for dealing with reaction time outliers.}, + author={Ratcliff, Roger}, + journal={Psychological bulletin}, + volume={114}, + number={3}, + pages={510}, + year={1993}, + publisher={American Psychological Association}, + doi = {10.1037/0033-2909.114.3.510} +} + +@book{mcelreath2020statistical, + title={Statistical rethinking: A Bayesian course with examples in {R} and Stan}, + author={McElreath, Richard}, + year={2020}, + publisher={CRC press} +} + +@Manual{rcore, + title = {{R}: A Language and Environment for Statistical Computing}, + author = {{R Core Team}}, + organization = {R Foundation for Statistical Computing}, + address = {Vienna, Austria}, + year = {2021}, + url = {https://www.R-project.org/} +} \ No newline at end of file From fa27f7de8494f5d94ac38df1681ddc7ab741a9f6 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?R=C3=A9mi=20Th=C3=A9riault?= <13123390+rempsyc@users.noreply.github.com> Date: Wed, 27 Sep 2023 20:13:12 -0400 Subject: [PATCH 22/34] shorten first page by one line to fit next section on next page for actual JOSE rendering --- papers/JOSE/paper.Rmd | 2 +- papers/JOSE/paper.log | 16 ++++++++-------- papers/JOSE/paper.md | 2 +- papers/JOSE/paper.pdf | Bin 195839 -> 195783 bytes .../JOSE/paper_files/figure-latex/model-1.pdf | Bin 5757 -> 5757 bytes vignettes/check_outliers.Rmd | 2 +- 6 files changed, 11 insertions(+), 11 deletions(-) diff --git a/papers/JOSE/paper.Rmd b/papers/JOSE/paper.Rmd index d2b4dbfe7..0351d0509 100644 --- a/papers/JOSE/paper.Rmd +++ b/papers/JOSE/paper.Rmd @@ -105,7 +105,7 @@ library(datawizard) # Summary -Beyond the challenge of keeping up-to-date with current best practices regarding the diagnosis and treatment of outliers, an additional difficulty arises concerning the mathematical implementation of the recommended methods. In this paper, we provide an overview of current recommendations and best practices and demonstrate how they can easily and conveniently be implemented in the R statistical computing software, using the *{performance}* package of the *easystats* ecosystem. We cover univariate, multivariate, and model-based statistical outlier detection methods, their recommended threshold, standard output, and plotting methods. We conclude with recommendations on the handling of outliers: the different theoretical types of outliers, whether to exclude or winsorize them, and the importance of transparency. +Beyond the challenge of keeping up-to-date with current best practices regarding the diagnosis and treatment of outliers, an additional difficulty arises concerning the mathematical implementation of the recommended methods. Here, we provide an overview of current recommendations and best practices and demonstrate how they can easily and conveniently be implemented in the R statistical computing software, using the *{performance}* package of the *easystats* ecosystem. We cover univariate, multivariate, and model-based statistical outlier detection methods, their recommended threshold, standard output, and plotting methods. We conclude by reviewing the different theoretical types of outliers, whether to exclude or winsorize them, and the importance of transparency. # Statement of Need diff --git a/papers/JOSE/paper.log b/papers/JOSE/paper.log index 046bb99c4..04911cf98 100644 --- a/papers/JOSE/paper.log +++ b/papers/JOSE/paper.log @@ -1,4 +1,4 @@ -This is XeTeX, Version 3.141592653-2.6-0.999995 (MiKTeX 23.5) (preloaded format=xelatex 2023.5.20) 27 SEP 2023 19:13 +This is XeTeX, Version 3.141592653-2.6-0.999995 (MiKTeX 23.5) (preloaded format=xelatex 2023.5.20) 27 SEP 2023 20:12 entering extended mode restricted \write18 enabled. %&-line parsing enabled. @@ -1268,7 +1268,7 @@ Package fancyhdr Warning: \headheight is too small (62.59596pt): (fancyhdr) \addtolength{\topmargin}{-1.71957pt}. LaTeX Font Info: Font shape `TU/lmss/m/it' in size <8> not available -(Font) Font shape `TU/lmss/m/sl' tried instead on input line 387. +(Font) Font shape `TU/lmss/m/sl' tried instead on input line 386. [1 ] @@ -1286,15 +1286,15 @@ Package fancyhdr Warning: \headheight is too small (62.59596pt): [2] LaTeX Font Info: Font shape `TU/lmtt/bx/n' in size <10> not available -(Font) Font shape `TU/lmtt/b/n' tried instead on input line 458. +(Font) Font shape `TU/lmtt/b/n' tried instead on input line 457. -Overfull \hbox (32.66139pt too wide) in paragraph at lines 474--474 +Overfull \hbox (32.66139pt too wide) in paragraph at lines 473--473 []\TU/lmtt/m/n/10 #> ---------------------------------------------------------- -------------------[] [] -Overfull \hbox (32.66139pt too wide) in paragraph at lines 483--483 +Overfull \hbox (32.66139pt too wide) in paragraph at lines 482--482 []\TU/lmtt/m/n/10 #> ---------------------------------------------------------- -------------------[] [] @@ -1366,19 +1366,19 @@ Package fancyhdr Warning: \headheight is too small (62.59596pt): (fancyhdr) \addtolength{\topmargin}{-1.71957pt}. [7] -Underfull \hbox (badness 1584) in paragraph at lines 919--925 +Underfull \hbox (badness 1584) in paragraph at lines 918--924 []\TU/lmr/m/n/10 Simmons, J. P., Nelson, L. D., & Simonsohn, U. (2011). False-p ositive psy- [] -Underfull \hbox (badness 3049) in paragraph at lines 919--925 +Underfull \hbox (badness 3049) in paragraph at lines 918--924 \TU/lmr/m/n/10 chology: Undisclosed flexibility in data collection and analysis allows pre- [] -Underfull \hbox (badness 3735) in paragraph at lines 919--925 +Underfull \hbox (badness 3735) in paragraph at lines 918--924 \TU/lmr/m/n/10 senting anything as significant. \TU/lmr/m/it/10 Psychological S cience\TU/lmr/m/n/10 , \TU/lmr/m/it/10 22\TU/lmr/m/n/10 (11), 1359–1366. [] diff --git a/papers/JOSE/paper.md b/papers/JOSE/paper.md index 983f9824d..cc4deedbd 100644 --- a/papers/JOSE/paper.md +++ b/papers/JOSE/paper.md @@ -93,7 +93,7 @@ csl: apa.csl # Summary -Beyond the challenge of keeping up-to-date with current best practices regarding the diagnosis and treatment of outliers, an additional difficulty arises concerning the mathematical implementation of the recommended methods. In this paper, we provide an overview of current recommendations and best practices and demonstrate how they can easily and conveniently be implemented in the R statistical computing software, using the *{performance}* package of the *easystats* ecosystem. We cover univariate, multivariate, and model-based statistical outlier detection methods, their recommended threshold, standard output, and plotting methods. We conclude with recommendations on the handling of outliers: the different theoretical types of outliers, whether to exclude or winsorize them, and the importance of transparency. +Beyond the challenge of keeping up-to-date with current best practices regarding the diagnosis and treatment of outliers, an additional difficulty arises concerning the mathematical implementation of the recommended methods. Here, we provide an overview of current recommendations and best practices and demonstrate how they can easily and conveniently be implemented in the R statistical computing software, using the *{performance}* package of the *easystats* ecosystem. We cover univariate, multivariate, and model-based statistical outlier detection methods, their recommended threshold, standard output, and plotting methods. We conclude by reviewing the different theoretical types of outliers, whether to exclude or winsorize them, and the importance of transparency. # Statement of Need diff --git a/papers/JOSE/paper.pdf b/papers/JOSE/paper.pdf index 76bf20f3be338d90a945ebc5d52f26f571724f2e..e892a13d2e9b4eead96bc1995cf98b0a41194e7b 100644 GIT binary patch delta 19834 zcmagEW00oN)+|`IZQHi1%eIX!+j`5kZQDkdx@_CFT{ZpPb0g-SnTePmJK~A`Ggq$6 zTx&l+Z?Ge8u>Q@!@PYs~CIJB$XBQ_kBU>1c^((xISTgRrX^lffm)ae~ibY7U>fKf* z6v&~1DsOA6Q#GCoqLn)}c~g%^*YBIwv@Ia` z3vbU^JFXs)Pp8e=6*ZbB^Nn=b)xwB@ymSU<$z{o>Y=;2t(ZEI2QY&A?-qP#+ign3= z#9PJt&}gded)YlJmq7V_)yntN@R_F9Im}%U(XwA{OqFkspD%L(iKDPTIxvux0}6q* zj9c?tu8=^qF>?%u+uivNb3R22%Ty4AAg9tjl=L2un zGtl8wvk(sIP-n%(I|QFjiu!k(gd=ee#+m+^<q93xu|tbfBebLNh^^d za(I|ySqxy7ZI)pb3FOdf9#H1or2=tF7Tfs7k$V>Y8sGMVbK|L&Kkn9&jGpM$uN#1nqO1VBT&km7#F@@|%2MeSAy1+PdmhQEfd;Zm!7t{$|NVNGPuBCD_z znG};`a%Ffd33q+wVrYcM4F6@;De*H~C^#U*Rf+O16ermZ>D@sVn-$W^EK6F*2sr`bowc7Muny1uyC1yo4qn&m8_LYE*MWWiW9_SJi5PnNubc6t^SzPG(-sW<=z 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kU!3qvDIV*?XIb0ZT|Lvt557jruW8-hw=73}P| Zic1oUN-By{)3{8HO$@nIRbBnvxB&1$DOdmi delta 165 zcmeyX^H*m>GrN+ZrJ=ErsV0}cZ+?nPVo9okhKrSvfswI+rI9&AZu3(1O+0L1w%O!Z z5m_j6bA!ly#yCdwDjom; diff --git a/vignettes/check_outliers.Rmd b/vignettes/check_outliers.Rmd index 804be2432..b4fe221ed 100644 --- a/vignettes/check_outliers.Rmd +++ b/vignettes/check_outliers.Rmd @@ -46,7 +46,7 @@ if (can_evaluate) { # Summary -Beyond the challenge of keeping up-to-date with current best practices regarding the diagnosis and treatment of outliers, an additional difficulty arises concerning the mathematical implementation of the recommended methods. In this paper, we provide an overview of current recommendations and best practices and demonstrate how they can easily and conveniently be implemented in the R statistical computing software, using the *{performance}* package of the *easystats* ecosystem. We cover univariate, multivariate, and model-based statistical outlier detection methods, their recommended threshold, standard output, and plotting methods. We conclude with recommendations on the handling of outliers: the different theoretical types of outliers, whether to exclude or winsorize them, and the importance of transparency. +Beyond the challenge of keeping up-to-date with current best practices regarding the diagnosis and treatment of outliers, an additional difficulty arises concerning the mathematical implementation of the recommended methods. In this vignette, we provide an overview of current recommendations and best practices and demonstrate how they can easily and conveniently be implemented in the R statistical computing software, using the *{performance}* package of the *easystats* ecosystem. We cover univariate, multivariate, and model-based statistical outlier detection methods, their recommended threshold, standard output, and plotting methods. We conclude with recommendations on the handling of outliers: the different theoretical types of outliers, whether to exclude or winsorize them, and the importance of transparency. # Statement of Need From 7a92bba0b35e0836d4480e05f482a75c49f29dda Mon Sep 17 00:00:00 2001 From: rempsyc Date: Tue, 3 Oct 2023 12:27:11 -0400 Subject: [PATCH 23/34] addresses #634 [skip ci] --- papers/JOSE/paper.Rmd | 4 ++-- vignettes/check_outliers.Rmd | 4 ++-- 2 files changed, 4 insertions(+), 4 deletions(-) diff --git a/papers/JOSE/paper.Rmd b/papers/JOSE/paper.Rmd index 0351d0509..4307a5001 100644 --- a/papers/JOSE/paper.Rmd +++ b/papers/JOSE/paper.Rmd @@ -119,7 +119,7 @@ The instructional materials that follow is aimed at an audience of researchers w # Identifying Outliers -Although many researchers attempt to identify outliers with measures based on the mean (e.g., _z_ scores), those methods are problematic because the mean and standard deviation themselves are not robust to the influence of outliers and they assume normally distributed data (i.e., a Gaussian distribution). Therefore, current guidelines recommend using robust methods to identify outliers, such as those relying on the median as opposed to the mean [@leys2019outliers; @leys2013outliers; @leys2018outliers]. +Although many researchers attempt to identify outliers with measures based on the mean (e.g., _z_ scores), those methods are problematic because the mean and standard deviation themselves are not robust to the influence of outliers and those methods also assume normally distributed data (i.e., a Gaussian distribution). Therefore, current guidelines recommend using robust methods to identify outliers, such as those relying on the median as opposed to the mean [@leys2019outliers; @leys2013outliers; @leys2018outliers]. Nonetheless, which exact outlier method to use depends on many factors. In some cases, eye-gauging odd observations can be an appropriate solution, though many researchers will favour algorithmic solutions to detect potential outliers, for example, based on a continuous value expressing the observation stands out from the others. @@ -250,7 +250,7 @@ The above section demonstrated how to identify outliers using the `check_outlier It is recommended to _keep_ observations which are expected to be part of the distribution of interest, even if they are outliers [@leys2019outliers]. However, if it is suspected that the outliers belong to an alternative distribution, then those observations could have a large impact on the results and call into question their robustness, especially if significance is conditional on their inclusion, so should be removed. -On the other hand, there are also outliers that cannot be detected by statistical tools, but should be found and removed. For example, if we are studying the effects of X on Y among teenagers and we have one observation from a 20-year-old, this observation might not be a _statistical outlier_, but it is an outlier in the _context_ of our research, and should be discarded to allow for valid inferences. +We should also keep in mind that there might be error outliers that are not detected by statistical tools, but should nonetheless be found and removed. For example, if we are studying the effects of X on Y among teenagers and we have one observation from a 20-year-old, this observation might not be a _statistical outlier_, but it is an outlier in the _context_ of our research, and should be discarded. We could call these observations *undetected* error outliers, in the sense that although they do not statistically stand out, they do not belong to the theoretical or empirical distribution of interest (e.g., teenagers). In this way, we should not blindly rely on statistical outlier detection methods; doing our due diligence to investigate undetected error outliers relative to our specific research question is also essential for valid inferences. ## Winsorization diff --git a/vignettes/check_outliers.Rmd b/vignettes/check_outliers.Rmd index b4fe221ed..f3ed6a616 100644 --- a/vignettes/check_outliers.Rmd +++ b/vignettes/check_outliers.Rmd @@ -60,7 +60,7 @@ The instructional materials that follow is aimed at an audience of researchers w # Identifying Outliers -Although many researchers attempt to identify outliers with measures based on the mean (e.g., _z_ scores), those methods are problematic because the mean and standard deviation themselves are not robust to the influence of outliers and they assume normally distributed data (i.e., a Gaussian distribution). Therefore, current guidelines recommend using robust methods to identify outliers, such as those relying on the median as opposed to the mean [@leys2019outliers; @leys2013outliers; @leys2018outliers]. +Although many researchers attempt to identify outliers with measures based on the mean (e.g., _z_ scores), those methods are problematic because the mean and standard deviation themselves are not robust to the influence of outliers and those methods also assume normally distributed data (i.e., a Gaussian distribution). Therefore, current guidelines recommend using robust methods to identify outliers, such as those relying on the median as opposed to the mean [@leys2019outliers; @leys2013outliers; @leys2018outliers]. Nonetheless, which exact outlier method to use depends on many factors. In some cases, eye-gauging odd observations can be an appropriate solution, though many researchers will favour algorithmic solutions to detect potential outliers, for example, based on a continuous value expressing the observation stands out from the others. @@ -239,7 +239,7 @@ The above section demonstrated how to identify outliers using the `check_outlier It is recommended to _keep_ observations which are expected to be part of the distribution of interest, even if they are outliers [@leys2019outliers]. However, if it is suspected that the outliers belong to an alternative distribution, then those observations could have a large impact on the results and call into question their robustness, especially if significance is conditional on their inclusion, so should be removed. -On the other hand, there are also outliers that cannot be detected by statistical tools, but should be found and removed. For example, if we are studying the effects of X on Y among teenagers and we have one observation from a 20-year-old, this observation might not be a _statistical outlier_, but it is an outlier in the _context_ of our research, and should be discarded to allow for valid inferences. +We should also keep in mind that there might be error outliers that are not detected by statistical tools, but should nonetheless be found and removed. For example, if we are studying the effects of X on Y among teenagers and we have one observation from a 20-year-old, this observation might not be a _statistical outlier_, but it is an outlier in the _context_ of our research, and should be discarded. We could call these observations *undetected* error outliers, in the sense that although they do not statistically stand out, they do not belong to the theoretical or empirical distribution of interest (e.g., teenagers). In this way, we should not blindly rely on statistical outlier detection methods; doing our due diligence to investigate undetected error outliers relative to our specific research question is also essential for valid inferences. ## Winsorization From 273be72e9f293cf125d5115c5e6cb5bfd0704692 Mon Sep 17 00:00:00 2001 From: rempsyc Date: Tue, 3 Oct 2023 13:40:55 -0400 Subject: [PATCH 24/34] addresses #635 --- papers/JOSE/paper.Rmd | 24 +- papers/JOSE/paper.log | 795 +++++++----------- papers/JOSE/paper.md | 6 +- papers/JOSE/paper.pdf | Bin 195783 -> 199510 bytes .../JOSE/paper_files/figure-latex/model-1.pdf | Bin 5757 -> 8475 bytes vignettes/check_outliers.Rmd | 14 +- 6 files changed, 316 insertions(+), 523 deletions(-) diff --git a/papers/JOSE/paper.Rmd b/papers/JOSE/paper.Rmd index 4307a5001..bbd9bcaad 100644 --- a/papers/JOSE/paper.Rmd +++ b/papers/JOSE/paper.Rmd @@ -109,7 +109,7 @@ Beyond the challenge of keeping up-to-date with current best practices regarding # Statement of Need -Real-life data often contain observations that can be considered *abnormal* when compared to the main population. The cause of it---be it because they belong to a different distribution (originating from a different generative process) or simply being extreme cases, statistically rare but not impossible---can be hard to assess, and the boundaries of "abnormal" difficult to define. +Real-life data often contain observations that can be considered *abnormal* when compared to the main population. The cause of it can be hard to assess and the boundaries of "abnormal", difficult to define---they may belong to a different distribution (originating from a different generative process) or simply be extreme cases, statistically rare but not impossible. Nonetheless, the improper handling of these outliers can substantially affect statistical model estimations, biasing effect estimations and weakening the models' predictive performance. It is thus essential to address this problem in a thoughtful manner. Yet, despite the existence of established recommendations and guidelines, many researchers still do not treat outliers in a consistent manner, or do so using inappropriate strategies [@simmons2011false; @leys2013outliers]. @@ -133,7 +133,11 @@ Importantly, whatever approach researchers choose remains a subjective decision, Researchers frequently attempt to identify outliers using measures of deviation from the center of a variable's distribution. One of the most popular such procedure is the _z_ score transformation, which computes the distance in standard deviation (SD) from the mean. However, as mentioned earlier, this popular method is not robust. Therefore, for univariate outliers, it is recommended to use the median along with the Median Absolute Deviation (MAD), which are more robust than the interquartile range or the mean and its standard deviation [@leys2019outliers; @leys2013outliers]. -Researchers can identify outliers based on robust (i.e., MAD-based) _z_ scores using the `check_outliers()` function of the *{performance}* package, by specifying `method = "zscore_robust"`.^[Note that `check_outliers()` only checks numeric variables.] Although @leys2013outliers suggest a default threshold of 2.5 and @leys2019outliers a threshold of 3, *{performance}* uses by default a less conservative threshold of ~3.29.^[3.29 is an approximation of the two-tailed critical value for _p_ < .001, obtained through `qnorm(p = 1 - 0.001 / 2)`. We chose this threshold for consistency with the thresholds of all our other methods.] That is, data points will be flagged as outliers if they go beyond +/- ~3.29 MAD. Users can adjust this threshold using the `threshold` argument, as demonstrated below. +Researchers can identify outliers based on robust (i.e., MAD-based) _z_ scores using the `check_outliers()` function of the *{performance}* package, by specifying `method = "zscore_robust"`.^[Note that `check_outliers()` only checks numeric variables.] Although @leys2013outliers suggest a default threshold of 2.5 and @leys2019outliers a threshold of 3, *{performance}* uses by default a less conservative threshold of ~3.29.^[3.29 is an approximation of the two-tailed critical value for _p_ < .001, obtained through `qnorm(p = 1 - 0.001 / 2)`. We chose this threshold for consistency with the thresholds of all our other methods.] That is, data points will be flagged as outliers if they go beyond +/- ~3.29 MAD. Users can adjust this threshold using the `threshold` argument. + +Below we provide example code using the `mtcars` dataset, which was extracted from the 1974 *Motor Trend* US magazine. The dataset contains fuel consumption and 10 characteristics of automobile design and performance for 32 different car models (see `?mtcars` for details). We chose this dataset because it is accessible from base R and familiar to many R users. We might want to conduct specific statistical analyses on this data set, say, _t_ tests or structural equation modelling, but first, we want to check for outliers that may influence those test results. + +Because the automobile names are stored as column names in `mtcars`, we first have to convert them to an ID column to benefit from the `check_outliers()` ID argument. Furthermore, we only really need a couple columns for this demonstration, so we choose the first four (`mpg` = Miles/(US) gallon; `cyl` = Number of cylinders; `disp` = Displacement; `hp` = Gross horsepower). Finally, because there are no outliers in this dataset, we add two artificial outliers before running our function. ```{r z_score} library(performance) @@ -146,7 +150,9 @@ outliers <- check_outliers(data, method = "zscore_robust", ID = "car") outliers ``` -The row numbers of the detected outliers can be obtained by using `which()` on the output object, which can be used for exclusions for example: +What we see is that `check_outliers()` with the robust _z_ score method detected two outliers: cases 33 and 34, which were the observations we added ourselves. They were flagged for two variables specifically: `mpg` (Miles/(US) gallon) and `cyl` (Number of cylinders), and the output provides their exact _z_ score for those variables. + +We describe how to deal with those cases in more details later in the paper, but should we want to exclude these detected outliers from the main dataset, we can extract row numbers using `which()` on the output object, which can then be used for indexing: ```{r} which(outliers) @@ -154,8 +160,6 @@ which(outliers) data_clean <- data[-which(outliers), ] ``` -All `check_outliers()` output objects possess a `plot()` method, meaning it is also possible to visualize the outliers using the generic `plot()` function on the resulting outlier object after loading the {see} package. - Other univariate methods are available, such as using the interquartile range (IQR), or based on different intervals, such as the Highest Density Interval (HDI) or the Bias Corrected and Accelerated Interval (BCI). These methods are documented and described in the function's [help page](). ## Multivariate Outliers @@ -173,6 +177,8 @@ outliers <- check_outliers(data, method = "mcd") outliers ``` +Here, we detected 9 multivariate outliers (i.e,. when looking at all variables of our dataset together). + Other multivariate methods are available, such as another type of robust Mahalanobis distance that in this case relies on an orthogonalized Gnanadesikan-Kettenring pairwise estimator [@gnanadesikan1972robust]. These methods are documented and described in the function's [help page](https://easystats.github.io/performance/reference/check_outliers.html). ## Model-Based Outliers @@ -181,11 +187,17 @@ Working with regression models creates the possibility of using model-based SOD In {performance}, two such model-based SOD methods are currently available: Cook's distance, for regular regression models, and Pareto, for Bayesian models. As such, `check_outliers()` can be applied directly on regression model objects, by simply specifying `method = "cook"` (or `method = "pareto"` for Bayesian models).^[Our default threshold for the Cook method is defined by `stats::qf(0.5, ncol(x), nrow(x) - ncol(x))`, which again is an approximation of the critical value for _p_ < .001 consistent with the thresholds of our other methods.] -```{r model, fig.cap = "Visual depiction of outliers based on Cook's distance (leverage and standardized residuals), based on the fitted model."} +```{r model} model <- lm(disp ~ mpg * disp, data = data) outliers <- check_outliers(model, method = "cook") outliers +``` + +Using the model-based outlier detection method, we identified a single outlier. + +All `check_outliers()` output objects possess a `plot()` method, meaning it is also possible to visualize the outliers using the generic `plot()` function on the resulting outlier object after loading the {see} package. +```{r model_fig, fig.cap = "Visual depiction of outliers based on Cook's distance (leverage and standardized residuals), based on the fitted model."} plot(outliers) ``` diff --git a/papers/JOSE/paper.log b/papers/JOSE/paper.log index 04911cf98..0de3a3a75 100644 --- a/papers/JOSE/paper.log +++ b/papers/JOSE/paper.log @@ -1,15 +1,15 @@ -This is XeTeX, Version 3.141592653-2.6-0.999995 (MiKTeX 23.5) (preloaded format=xelatex 2023.5.20) 27 SEP 2023 20:12 +This is XeTeX, Version 3.141592653-2.6-0.999995 (TeX Live 2023) (preloaded format=xelatex 2023.9.14) 3 OCT 2023 12:56 entering extended mode restricted \write18 enabled. %&-line parsing enabled. -**./paper.tex -(paper.tex -LaTeX2e <2022-11-01> patch level 1 -L3 programming layer <2023-05-15> (C:\Users\there\AppData\Local\Programs\MiKTeX -\tex/latex/base\article.cls -Document Class: article 2022/07/02 v1.4n Standard LaTeX document class -(C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/base\size10.clo -File: size10.clo 2022/07/02 v1.4n Standard LaTeX file 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Package hyperref Info: Option `breaklinks' set `true' on input line 12. -(C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/caption\caption.sty -Package: caption 2023/03/12 v3.6j Customizing captions (AR) -(C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/caption\caption3.sty -Package: caption3 2023/03/12 v2.4 caption3 kernel (AR) +(c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/caption/caption.sty +Package: caption 2023/07/31 v3.6n Customizing captions (AR) +(c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/caption/caption3.sty +Package: caption3 2023/07/31 v2.4d caption3 kernel (AR) \caption@tempdima=\dimen260 \captionmargin=\dimen261 \caption@leftmargin=\dimen262 @@ -559,22 +400,19 @@ Package caption Info: Standard document class detected. \c@caption@flags=\count298 \c@continuedfloat=\count299 Package caption Info: hyperref package is loaded. -) -(C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/tcolorbox\tcolorbox.sty -Package: tcolorbox 2023/03/17 version 6.0.3 text color boxes -(C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/tools\verbatim.sty +) (c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/tcolorbox/tcolorbox.sty +Package: tcolorbox 2023/06/19 version 6.0.4 text color boxes +(c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/tools/verbatim.sty Package: verbatim 2022-07-02 v1.5u LaTeX2e package for verbatim enhancements -\every@verbatim=\toks30 -\verbatim@line=\toks31 +\every@verbatim=\toks31 +\verbatim@line=\toks32 \verbatim@in@stream=\read3 -) (C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/environ\environ.sty +) (c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/environ/environ.sty Package: environ 2014/05/04 v0.3 A new way to define environments - -(C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/trimspaces\trimspaces.s -ty +(c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/trimspaces/trimspaces.sty Package: trimspaces 2009/09/17 v1.1 Trim spaces around a token list ) -\@envbody=\toks32 +\@envbody=\toks33 ) \tcb@titlebox=\box64 \tcb@upperbox=\box65 @@ -587,30 +425,30 @@ Package: trimspaces 2009/09/17 v1.1 Trim spaces around a token list \tcb@temp=\box69 \tcb@temp=\box70 \tcb@temp=\box71 -) (C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/amsfonts\amssymb.sty +) (c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/amsfonts/amssymb.sty Package: amssymb 2013/01/14 v3.01 AMS font symbols -(C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/amsfonts\amsfonts.sty +(c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/amsfonts/amsfonts.sty Package: amsfonts 2013/01/14 v3.01 Basic AMSFonts support -\@emptytoks=\toks33 +\@emptytoks=\toks34 \symAMSa=\mathgroup4 \symAMSb=\mathgroup5 LaTeX Font Info: Redeclaring math symbol \hbar on input line 98. 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LaTeX Info: Redefining \] on input line 2954. -) (C:\Users\there\AppData\Local\Programs\MiKTeX\tex/generic/iftex\ifxetex.sty +) (c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/generic/iftex/ifxetex.sty Package: ifxetex 2019/10/25 v0.7 ifxetex legacy package. Use iftex instead. -) (C:\Users\there\AppData\Local\Programs\MiKTeX\tex/generic/iftex\ifluatex.sty +) (c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/generic/iftex/ifluatex.sty Package: ifluatex 2019/10/25 v1.5 ifluatex legacy package. Use iftex instead. -) (C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/seqsplit\seqsplit.sty -Package: seqsplit 2006/08/07 v0.1 Splitting long sequences (DNA, RNA, proteins, - etc.) -) (C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/base\fixltx2e.sty +) (c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/seqsplit/seqsplit.sty +Package: seqsplit 2006/08/07 v0.1 Splitting long sequences (DNA, RNA, proteins, etc.) +) (c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/base/fixltx2e.sty Package: fixltx2e 2016/12/29 v2.1a fixes to LaTeX (obsolete) Applying: [2015/01/01] Old fixltx2e package on input line 46. @@ -676,14 +513,14 @@ Package fixltx2e Warning: fixltx2e is not required with releases after 2015 (fixltx2e) See the latexrelease package for details. 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Use iftex instead. \Gm@layoutheight=\dimen282 \Gm@layouthoffset=\dimen283 \Gm@layoutvoffset=\dimen284 -\Gm@dimlist=\toks39 -(C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/geometry\geometry.cfg)) -(C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/fancyhdr\fancyhdr.sty +\Gm@dimlist=\toks40 +) (c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/fancyhdr/fancyhdr.sty Package: fancyhdr 2022/11/09 v4.1 Extensive control of page headers and footers - \f@nch@headwidth=\skip83 \f@nch@O@elh=\skip84 \f@nch@O@erh=\skip85 @@ -957,17 +776,12 @@ Package: fancyhdr 2022/11/09 v4.1 Extensive control of page headers and footers \f@nch@O@erf=\skip89 \f@nch@O@olf=\skip90 \f@nch@O@orf=\skip91 -) -(C:\Users\there\AppData\Local\Programs\MiKTeX\tex/xelatex/mathspec\mathspec.sty -Package: mathspec 2016/12/22 v0.2b LaTeX Package (Mathematics font selection fo -r XeLaTeX) -(C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/fontspec\fontspec.sty +) (c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/xelatex/mathspec/mathspec.sty +Package: mathspec 2016/12/22 v0.2b LaTeX Package (Mathematics font selection for XeLaTeX) +(c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/fontspec/fontspec.sty Package: fontspec 2022/01/15 v2.8a Font selection for XeLaTeX and LuaLaTeX - -(C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/fontspec\fontspec-xetex -.sty -Package: fontspec-xetex 2022/01/15 v2.8a Font selection for XeLaTeX and LuaLaTe -X +(c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/fontspec/fontspec-xetex.sty +Package: fontspec-xetex 2022/01/15 v2.8a Font selection for XeLaTeX and LuaLaTeX \l__fontspec_script_int=\count448 \l__fontspec_language_int=\count449 \l__fontspec_strnum_int=\count450 @@ -982,15 +796,13 @@ X \l__fontspec_tmpa_dim=\dimen285 \l__fontspec_tmpb_dim=\dimen286 \l__fontspec_tmpc_dim=\dimen287 -(C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/base\fontenc.sty +(c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/base/fontenc.sty Package: fontenc 2021/04/29 v2.0v Standard LaTeX package -) (C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/fontspec\fontspec.cfg -))) (C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/xkeyval\xkeyval.sty +) (c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/fontspec/fontspec.cfg))) (c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/xkeyval/xkeyval.sty Package: xkeyval 2022/06/16 v2.9 package option processing (HA) -(C:\Users\there\AppData\Local\Programs\MiKTeX\tex/generic/xkeyval\xkeyval.tex ( -C:\Users\there\AppData\Local\Programs\MiKTeX\tex/generic/xkeyval\xkvutils.tex -\XKV@toks=\toks40 -\XKV@tempa@toks=\toks41 +(c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/generic/xkeyval/xkeyval.tex (c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/generic/xkeyval/xkvutils.tex +\XKV@toks=\toks41 +\XKV@tempa@toks=\toks42 ) \XKV@depth=\count459 File: xkeyval.tex 2014/12/03 v2.7a key=value parser (HA) @@ -998,46 +810,35 @@ File: xkeyval.tex 2014/12/03 v2.7a key=value parser (HA) \c@eu@=\count460 \c@eu@i=\count461 \c@mkern=\count462 -) (C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/upquote\upquote.sty -Package: upquote 2012/04/19 v1.3 upright-quote and grave-accent glyphs in verba -tim -(C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/base\textcomp.sty -Package: textcomp 2020/02/02 v2.0n Standard LaTeX package -)) -(C:\Users\there\AppData\Local\Programs\MiKTeX\tex/latex/microtype\microtype.sty +) (c:/Users/rempsyc/AppData/Roaming/TinyTeX/texmf-dist/tex/latex/microtype/microtype.sty Package: microtype 2023/03/13 v3.1a Micro-typographical refinements (RS) -\MT@toks=\toks42 +\MT@toks=\toks43 \MT@tempbox=\box75 \MT@count=\count463 LaTeX Info: Redefining \noprotrusionifhmode on input line 1059. 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[5] -File: C:/Users/there/AppData/Local/R/win-library/4.3/rticles/rmarkdown/template -s/joss/resources/JOSE-logo.png Graphic file (type bmp) - +File: D:/Rpackages/rticles/rmarkdown/templates/joss/resources/JOSE-logo.png Graphic file (type bmp) + Package fancyhdr Warning: \headheight is too small (62.59596pt): (fancyhdr) Make it at least 64.31554pt, for example: (fancyhdr) \setlength{\headheight}{64.31554pt}. (fancyhdr) You might also make \topmargin smaller to compensate: - (fancyhdr) \addtolength{\topmargin}{-1.71957pt}. [6] -File: C:/Users/there/AppData/Local/R/win-library/4.3/rticles/rmarkdown/template -s/joss/resources/JOSE-logo.png Graphic file (type bmp) - +File: D:/Rpackages/rticles/rmarkdown/templates/joss/resources/JOSE-logo.png Graphic file (type bmp) + Package fancyhdr Warning: \headheight is too small (62.59596pt): (fancyhdr) Make it at least 64.31554pt, for example: (fancyhdr) \setlength{\headheight}{64.31554pt}. (fancyhdr) You might also make \topmargin smaller to compensate: - (fancyhdr) \addtolength{\topmargin}{-1.71957pt}. [7] -Underfull \hbox (badness 1584) in paragraph at lines 918--924 -[]\TU/lmr/m/n/10 Simmons, J. P., Nelson, L. D., & Simonsohn, U. (2011). False-p -ositive psy- +Underfull \hbox (badness 1584) in paragraph at lines 926--932 +[]\TU/lmr/m/n/10 Simmons, J. P., Nelson, L. D., & Simonsohn, U. (2011). False-positive psy- [] -Underfull \hbox (badness 3049) in paragraph at lines 918--924 -\TU/lmr/m/n/10 chology: Undisclosed flexibility in data collection and analysis - allows pre- +Underfull \hbox (badness 3049) in paragraph at lines 926--932 +\TU/lmr/m/n/10 chology: Undisclosed flexibility in data collection and analysis allows pre- [] -Underfull \hbox (badness 3735) in paragraph at lines 918--924 -\TU/lmr/m/n/10 senting anything as significant. \TU/lmr/m/it/10 Psychological S -cience\TU/lmr/m/n/10 , \TU/lmr/m/it/10 22\TU/lmr/m/n/10 (11), 1359–1366. +Underfull \hbox (badness 3735) in paragraph at lines 926--932 +\TU/lmr/m/n/10 senting anything as significant. \TU/lmr/m/it/10 Psychological Science\TU/lmr/m/n/10 , \TU/lmr/m/it/10 22\TU/lmr/m/n/10 (11), 1359–1366. [] -File: C:/Users/there/AppData/Local/R/win-library/4.3/rticles/rmarkdown/template -s/joss/resources/JOSE-logo.png Graphic file (type bmp) - +File: D:/Rpackages/rticles/rmarkdown/templates/joss/resources/JOSE-logo.png Graphic file (type bmp) + Package fancyhdr Warning: \headheight is too small (62.59596pt): (fancyhdr) Make it at least 64.31554pt, for example: (fancyhdr) \setlength{\headheight}{64.31554pt}. (fancyhdr) You might also make \topmargin smaller to compensate: +(fancyhdr) \addtolength{\topmargin}{-1.71957pt}. + +[8] +File: D:/Rpackages/rticles/rmarkdown/templates/joss/resources/JOSE-logo.png Graphic file (type bmp) + +Package fancyhdr Warning: \headheight is too small (62.59596pt): +(fancyhdr) Make it at least 64.31554pt, for example: +(fancyhdr) \setlength{\headheight}{64.31554pt}. +(fancyhdr) You might also make \topmargin smaller to compensate: (fancyhdr) \addtolength{\topmargin}{-1.71957pt}. -[8] (paper.aux) +[9] (./paper.aux) + *********** +LaTeX2e <2023-06-01> patch level 1 +L3 programming layer <2023-08-29> + *********** Package rerunfilecheck Info: File `paper.out' has not changed. (rerunfilecheck) Checksum: EEBE57815200557F8EDD73A1BF6F9118;2043. Package logreq Info: Writing requests to 'paper.run.xml'. @@ -1403,12 +1174,12 @@ Package logreq Info: Writing requests to 'paper.run.xml'. ) Here is how much of TeX's memory you used: - 37316 strings out of 411547 - 752904 string characters out of 5819451 - 1873476 words of memory out of 5000000 - 56952 multiletter control sequences out of 15000+600000 - 519199 words of font info for 85 fonts, out of 8000000 for 9000 - 1348 hyphenation exceptions out of 8191 - 84i,12n,81p,1196b,850s stack positions out of 10000i,1000n,20000p,200000b,200000s - -Output written on paper.pdf (8 pages). + 36963 strings out of 477589 + 757118 string characters out of 5817003 + 1940432 words of memory out of 5000000 + 57602 multiletter control sequences out of 15000+600000 + 564981 words of font info for 89 fonts, out of 8000000 for 9000 + 14 hyphenation exceptions out of 8191 + 84i,12n,87p,1194b,850s stack positions out of 10000i,1000n,20000p,200000b,200000s + +Output written on paper.pdf (9 pages). diff --git a/papers/JOSE/paper.md b/papers/JOSE/paper.md index cc4deedbd..c376cb3e2 100644 --- a/papers/JOSE/paper.md +++ b/papers/JOSE/paper.md @@ -97,7 +97,7 @@ Beyond the challenge of keeping up-to-date with current best practices regarding # Statement of Need -Real-life data often contain observations that can be considered *abnormal* when compared to the main population. The cause of it---be it because they belong to a different distribution (originating from a different generative process) or simply being extreme cases, statistically rare but not impossible---can be hard to assess, and the boundaries of "abnormal" difficult to define. +Real-life data often contain observations that can be considered *abnormal* when compared to the main population. The cause of it can be hard to assess and the boundaries of "abnormal", difficult to define---they may belong to a different distribution (originating from a different generative process) or simply be extreme cases, statistically rare but not impossible. Nonetheless, the improper handling of these outliers can substantially affect statistical model estimations, biasing effect estimations and weakening the models' predictive performance. It is thus essential to address this problem in a thoughtful manner. Yet, despite the existence of established recommendations and guidelines, many researchers still do not treat outliers in a consistent manner, or do so using inappropriate strategies [@simmons2011false; @leys2013outliers]. @@ -107,7 +107,7 @@ The instructional materials that follow is aimed at an audience of researchers w # Identifying Outliers -Although many researchers attempt to identify outliers with measures based on the mean (e.g., _z_ scores), those methods are problematic because the mean and standard deviation themselves are not robust to the influence of outliers and they assume normally distributed data (i.e., a Gaussian distribution). Therefore, current guidelines recommend using robust methods to identify outliers, such as those relying on the median as opposed to the mean [@leys2019outliers; @leys2013outliers; @leys2018outliers]. +Although many researchers attempt to identify outliers with measures based on the mean (e.g., _z_ scores), those methods are problematic because the mean and standard deviation themselves are not robust to the influence of outliers and those methods also assume normally distributed data (i.e., a Gaussian distribution). Therefore, current guidelines recommend using robust methods to identify outliers, such as those relying on the median as opposed to the mean [@leys2019outliers; @leys2013outliers; @leys2018outliers]. Nonetheless, which exact outlier method to use depends on many factors. In some cases, eye-gauging odd observations can be an appropriate solution, though many researchers will favour algorithmic solutions to detect potential outliers, for example, based on a continuous value expressing the observation stands out from the others. @@ -296,7 +296,7 @@ The above section demonstrated how to identify outliers using the `check_outlier It is recommended to _keep_ observations which are expected to be part of the distribution of interest, even if they are outliers [@leys2019outliers]. However, if it is suspected that the outliers belong to an alternative distribution, then those observations could have a large impact on the results and call into question their robustness, especially if significance is conditional on their inclusion, so should be removed. -On the other hand, there are also outliers that cannot be detected by statistical tools, but should be found and removed. For example, if we are studying the effects of X on Y among teenagers and we have one observation from a 20-year-old, this observation might not be a _statistical outlier_, but it is an outlier in the _context_ of our research, and should be discarded to allow for valid inferences. +We should also keep in mind that there might be error outliers that are not detected by statistical tools, but should nonetheless be found and removed. For example, if we are studying the effects of X on Y among teenagers and we have one observation from a 20-year-old, this observation might not be a _statistical outlier_, but it is an outlier in the _context_ of our research, and should be discarded. We could call these observations *undetected* error outliers, in the sense that although they do not statistically stand out, they do not belong to the theoretical or empirical distribution of interest (e.g., teenagers). 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z1pU9|xCvLW$=TFK4Nt<8;CNG8F#!wW0jx3r9)R3faXN9}J@*of*{1YSm zlLrx?zw-!KBB;Q0|FW0>LLe*#c8GCE8!tXz2!INX;ybc&;f3-6P$9BWFo0wBkSz|R z)9DNdPjezLY(a>G!{R|AgeQPRh7*HG0scQF08spL0%35J@LUu(6iLA0K_mv_=;4Gw F{s{p*{Nw-t diff --git a/vignettes/check_outliers.Rmd b/vignettes/check_outliers.Rmd index f3ed6a616..64231fe8f 100644 --- a/vignettes/check_outliers.Rmd +++ b/vignettes/check_outliers.Rmd @@ -74,7 +74,11 @@ Importantly, whatever approach researchers choose remains a subjective decision, Researchers frequently attempt to identify outliers using measures of deviation from the center of a variable's distribution. One of the most popular such procedure is the _z_ score transformation, which computes the distance in standard deviation (SD) from the mean. However, as mentioned earlier, this popular method is not robust. Therefore, for univariate outliers, it is recommended to use the median along with the Median Absolute Deviation (MAD), which are more robust than the interquartile range or the mean and its standard deviation [@leys2019outliers; @leys2013outliers]. -Researchers can identify outliers based on robust (i.e., MAD-based) _z_ scores using the `check_outliers()` function of the *{performance}* package, by specifying `method = "zscore_robust"`.^[Note that `check_outliers()` only checks numeric variables.] Although @leys2013outliers suggest a default threshold of 2.5 and @leys2019outliers a threshold of 3, *{performance}* uses by default a less conservative threshold of ~3.29.^[3.29 is an approximation of the two-tailed critical value for _p_ < .001, obtained through `qnorm(p = 1 - 0.001 / 2)`. We chose this threshold for consistency with the thresholds of all our other methods.] That is, data points will be flagged as outliers if they go beyond +/- ~3.29 MAD. Users can adjust this threshold using the `threshold` argument, as demonstrated below. +Researchers can identify outliers based on robust (i.e., MAD-based) _z_ scores using the `check_outliers()` function of the *{performance}* package, by specifying `method = "zscore_robust"`.^[Note that `check_outliers()` only checks numeric variables.] Although @leys2013outliers suggest a default threshold of 2.5 and @leys2019outliers a threshold of 3, *{performance}* uses by default a less conservative threshold of ~3.29.^[3.29 is an approximation of the two-tailed critical value for _p_ < .001, obtained through `qnorm(p = 1 - 0.001 / 2)`. We chose this threshold for consistency with the thresholds of all our other methods.] That is, data points will be flagged as outliers if they go beyond +/- ~3.29 MAD. Users can adjust this threshold using the `threshold` argument. + +Below we provide example code using the `mtcars` dataset, which was extracted from the 1974 *Motor Trend* US magazine. The dataset contains fuel consumption and 10 characteristics of automobile design and performance for 32 different car models (see `?mtcars` for details). We chose this dataset because it is accessible from base R and familiar to many R users. We might want to conduct specific statistical analyses on this data set, say, _t_ tests or structural equation modelling, but first, we want to check for outliers that may influence those test results. + +Because the automobile names are stored as column names in `mtcars`, we first have to convert them to an ID column to benefit from the `check_outliers()` ID argument. Furthermore, we only really need a couple columns for this demonstration, so we choose the first four (`mpg` = Miles/(US) gallon; `cyl` = Number of cylinders; `disp` = Displacement; `hp` = Gross horsepower). Finally, because there are no outliers in this dataset, we add two artificial outliers before running our function. ```{r z_score} library(performance) @@ -87,7 +91,9 @@ outliers <- check_outliers(data, method = "zscore_robust", ID = "car") outliers ``` -The row numbers of the detected outliers can be obtained by using `which()` on the output object, which can be used for exclusions for example: +What we see is that `check_outliers()` with the robust _z_ score method detected two outliers: cases 33 and 34, which were the observations we added ourselves. They were flagged for two variables specifically: `mpg` (Miles/(US) gallon) and `cyl` (Number of cylinders), and the output provides their exact _z_ score for those variables. + +We describe how to deal with those cases in more details later in the paper, but should we want to exclude these detected outliers from the main dataset, we can extract row numbers using `which()` on the output object, which can then be used for indexing: ```{r} which(outliers) @@ -127,6 +133,8 @@ outliers <- check_outliers(data, method = "mcd") outliers ``` +Here, we detected 9 multivariate outliers (i.e,. when looking at all variables of our dataset together). + ```{r multivariate_plot, eval=FALSE} plot(outliers) ``` @@ -154,6 +162,8 @@ outliers plot(outliers) ``` +Using the model-based outlier detection method, we identified a single outlier. + Table 1 below summarizes which methods to use in which cases, and with what threshold. ```{r, echo=FALSE} From 6d8d3bb473e2093593a87e152c73936907eaf3cc Mon Sep 17 00:00:00 2001 From: rempsyc Date: Wed, 4 Oct 2023 10:49:35 -0400 Subject: [PATCH 25/34] fix failing checks --- inst/WORDLIST | 21 ++++++++++++++----- vignettes/check_outliers.Rmd | 39 ++++++++++++++++++++---------------- 2 files changed, 38 insertions(+), 22 deletions(-) diff --git a/inst/WORDLIST b/inst/WORDLIST index adf602827..57591d316 100644 --- a/inst/WORDLIST +++ b/inst/WORDLIST @@ -9,6 +9,7 @@ Ankerst Archimbaud Arel Asq +BCI BFBayesFactor BMJ Baayen @@ -75,6 +76,7 @@ Gazen Gelman Gnanadesikan Guilford +HDI HJ Hastie Herron @@ -110,10 +112,10 @@ Killeen Kliegl Kristensen Kullback -Lakens LOF LOGLOSS LOOIC +Lakens Laniado Leibler Lemeshow @@ -123,6 +125,7 @@ Leys Lillo Liu Lomax +MADs MSA Maddala Magee @@ -148,6 +151,7 @@ Nakagawa's Nordhausen Normed ORCID +OSF Olkin PNFI Pek @@ -210,6 +214,7 @@ WAIC WMK Weisberg Windmeijer +Winsorization Witten Xu YL @@ -237,6 +242,7 @@ brmsfit cauchy clusterable concurvity +datawizard dbscan der detrend @@ -252,20 +258,17 @@ fpsyg gam geoms ggplot -github gjo glm glmmTMB glmrob grey heteroskedasticity -homoskedasticity homoscedasticity +homoskedasticity https intra intraclass -io -ize joss kmeans lavaan @@ -285,18 +288,22 @@ models’ multicollinearity multimodel multiresponse +multivariable nd nonnest overfitted patilindrajeets poisson preprint +priori pscl quared quartile quartiles rOpenSci +recoding rempsyc +reproducibility rescaling rma rmarkdown @@ -308,6 +315,7 @@ se smicd sphericity strengejacke +suboptimal subscale subscales theoreritcal @@ -317,5 +325,8 @@ und underfitted underfitting visualisation +winsorization +winsorize +winsorized xy youtube diff --git a/vignettes/check_outliers.Rmd b/vignettes/check_outliers.Rmd index 64231fe8f..3c2199350 100644 --- a/vignettes/check_outliers.Rmd +++ b/vignettes/check_outliers.Rmd @@ -8,7 +8,7 @@ output: bibliography: paper.bib vignette: > \usepackage[utf8]{inputenc} - %\VignetteIndexEntry{Checking model assumption - linear models} + %\VignetteIndexEntry{Checking outliers with *performance*} %\VignetteEngine{knitr::rmarkdown} editor_options: chunk_output_type: console @@ -110,10 +110,10 @@ plot(outliers) ```{r univariate_implicit, fig.cap = "Visual depiction of outliers using the robust z-score method. The distance represents an aggregate score for variables mpg, cyl, disp, and hp.", echo=FALSE} library(see) -plot(outliers) + +plot(outliers) + ggplot2::theme(axis.text.x = ggplot2::element_text( angle = 45, size = 7 -)) + )) ``` Other univariate methods are available, such as using the interquartile range (IQR), or based on different intervals, such as the Highest Density Interval (HDI) or the Bias Corrected and Accelerated Interval (BCI). These methods are documented and described in the function's [help page](). @@ -140,10 +140,10 @@ plot(outliers) ``` ```{r multivariate_implicit, fig.cap = "Visual depiction of outliers using the Minimum Covariance Determinant (MCD) method, a robust version of the Mahalanobis distance. The distance represents the MCD scores for variables mpg, cyl, disp, and hp.", echo=FALSE} -plot(outliers) + +plot(outliers) + ggplot2::theme(axis.text.x = ggplot2::element_text( angle = 45, size = 7 -)) + )) ``` Other multivariate methods are available, such as another type of robust Mahalanobis distance that in this case relies on an orthogonalized Gnanadesikan-Kettenring pairwise estimator [@gnanadesikan1972robust]. These methods are documented and described in the function's [help page](https://easystats.github.io/performance/reference/check_outliers.html). @@ -169,21 +169,26 @@ Table 1 below summarizes which methods to use in which cases, and with what thre ```{r, echo=FALSE} df <- data.frame( `Statistical Test` = c( - "Supported regression model", - "Structural Equation Modeling (or other unsupported model)", - "Simple test with few variables (*t* test, correlation, etc.)"), + "Supported regression model", + "Structural Equation Modeling (or other unsupported model)", + "Simple test with few variables (*t* test, correlation, etc.)" + ), `Diagnosis Method` = c( - "**Model-based**: Cook (or Pareto for Bayesian models)", - "**Multivariate**: Minimum Covariance Determinant (MCD)", - "**Univariate**: robust *z* scores (MAD)"), + "**Model-based**: Cook (or Pareto for Bayesian models)", + "**Multivariate**: Minimum Covariance Determinant (MCD)", + "**Univariate**: robust *z* scores (MAD)" + ), `Recommended Threshold` = c( - "`qf(0.5, ncol(x), nrow(x) - ncol(x))` (or 0.7 for Pareto)", - "`qchisq(p = 1 - 0.001, df = ncol(x))`", - "`qnorm(p = 1 - 0.001 / 2)`, ~ 3.29") + "`qf(0.5, ncol(x), nrow(x) - ncol(x))` (or 0.7 for Pareto)", + "`qchisq(p = 1 - 0.001, df = ncol(x))`", + "`qnorm(p = 1 - 0.001 / 2)`, ~ 3.29" + ) ) knitr::kable( - df, col.names = gsub("[.]", " ", names(df)), - caption = "Summary of Statistical Outlier Detection Methods Recommendations.", longtable = TRUE) + df, + col.names = gsub("[.]", " ", names(df)), + caption = "Summary of Statistical Outlier Detection Methods Recommendations.", longtable = TRUE +) ``` ## Cook's Distance vs. MCD @@ -258,7 +263,7 @@ _Removing_ outliers can in this case be a valid strategy, and ideally one would The _easystats_ ecosystem makes it easy to incorporate this step into your workflow through the `winsorize()` function of *{datawizard}*, a lightweight R package to facilitate data wrangling and statistical transformations [@patil2022datawizard]. This procedure will bring back univariate outliers within the limits of 'acceptable' values, based either on the percentile, the _z_ score, or its robust alternative based on the MAD. ```{r winsorization} -data[1501:1502, ] # See outliers rows +data[1501:1502, ] # See outliers rows # Winsorizing using the MAD library(datawizard) winsorized_data <- winsorize(data, method = "zscore", robust = TRUE, threshold = 3) From 46e85758f6ce3ff075c44ace360cbd53a2fab3b7 Mon Sep 17 00:00:00 2001 From: rempsyc Date: Wed, 4 Oct 2023 11:26:11 -0400 Subject: [PATCH 26/34] render .md --- papers/JOSE/paper.log | 40 +++++++++--------- papers/JOSE/paper.md | 21 ++++++--- papers/JOSE/paper.pdf | Bin 199510 -> 202133 bytes .../paper_files/figure-latex/model_fig-1.pdf | Bin 0 -> 8480 bytes 4 files changed, 36 insertions(+), 25 deletions(-) create mode 100644 papers/JOSE/paper_files/figure-latex/model_fig-1.pdf diff --git a/papers/JOSE/paper.log b/papers/JOSE/paper.log index 0de3a3a75..b1a43ab5f 100644 --- a/papers/JOSE/paper.log +++ b/papers/JOSE/paper.log @@ -1,4 +1,4 @@ -This is XeTeX, Version 3.141592653-2.6-0.999995 (TeX Live 2023) (preloaded format=xelatex 2023.9.14) 3 OCT 2023 12:56 +This is XeTeX, Version 3.141592653-2.6-0.999995 (TeX Live 2023) (preloaded format=xelatex 2023.9.14) 4 OCT 2023 11:22 entering extended mode restricted \write18 enabled. %&-line parsing enabled. @@ -1066,14 +1066,14 @@ Package fancyhdr Warning: \headheight is too small (62.59596pt): [2] LaTeX Font Info: Font shape `TU/lmtt/bx/n' in size <10> not available -(Font) Font shape `TU/lmtt/b/n' tried instead on input line 458. +(Font) Font shape `TU/lmtt/b/n' tried instead on input line 477. -Overfull \hbox (32.66139pt too wide) in paragraph at lines 474--474 +Overfull \hbox (32.66139pt too wide) in paragraph at lines 493--493 []\TU/lmtt/m/n/10 #> -----------------------------------------------------------------------------[] [] -Overfull \hbox (32.66139pt too wide) in paragraph at lines 483--483 +Overfull \hbox (32.66139pt too wide) in paragraph at lines 502--502 []\TU/lmtt/m/n/10 #> -----------------------------------------------------------------------------[] [] @@ -1097,8 +1097,8 @@ Package fancyhdr Warning: \headheight is too small (62.59596pt): (fancyhdr) \addtolength{\topmargin}{-1.71957pt}. [4] -File: paper_files/figure-latex/model-1.pdf Graphic file (type pdf) - +File: paper_files/figure-latex/model_fig-1.pdf Graphic file (type pdf) + File: D:/Rpackages/rticles/rmarkdown/templates/joss/resources/JOSE-logo.png Graphic file (type bmp) @@ -1129,17 +1129,27 @@ Package fancyhdr Warning: \headheight is too small (62.59596pt): (fancyhdr) \addtolength{\topmargin}{-1.71957pt}. [7] -Underfull \hbox (badness 1584) in paragraph at lines 926--932 +File: D:/Rpackages/rticles/rmarkdown/templates/joss/resources/JOSE-logo.png Graphic file (type bmp) + + +Package fancyhdr Warning: \headheight is too small (62.59596pt): +(fancyhdr) Make it at least 64.31554pt, for example: +(fancyhdr) \setlength{\headheight}{64.31554pt}. +(fancyhdr) You might also make \topmargin smaller to compensate: +(fancyhdr) \addtolength{\topmargin}{-1.71957pt}. + +[8] +Underfull \hbox (badness 1584) in paragraph at lines 959--965 []\TU/lmr/m/n/10 Simmons, J. P., Nelson, L. D., & Simonsohn, U. (2011). False-positive psy- [] -Underfull \hbox (badness 3049) in paragraph at lines 926--932 +Underfull \hbox (badness 3049) in paragraph at lines 959--965 \TU/lmr/m/n/10 chology: Undisclosed flexibility in data collection and analysis allows pre- [] -Underfull \hbox (badness 3735) in paragraph at lines 926--932 +Underfull \hbox (badness 3735) in paragraph at lines 959--965 \TU/lmr/m/n/10 senting anything as significant. \TU/lmr/m/it/10 Psychological Science\TU/lmr/m/n/10 , \TU/lmr/m/it/10 22\TU/lmr/m/n/10 (11), 1359–1366. [] @@ -1152,16 +1162,6 @@ Package fancyhdr Warning: \headheight is too small (62.59596pt): (fancyhdr) You might also make \topmargin smaller to compensate: (fancyhdr) \addtolength{\topmargin}{-1.71957pt}. -[8] -File: D:/Rpackages/rticles/rmarkdown/templates/joss/resources/JOSE-logo.png Graphic file (type bmp) - - -Package fancyhdr Warning: \headheight is too small (62.59596pt): -(fancyhdr) Make it at least 64.31554pt, for example: -(fancyhdr) \setlength{\headheight}{64.31554pt}. -(fancyhdr) You might also make \topmargin smaller to compensate: -(fancyhdr) \addtolength{\topmargin}{-1.71957pt}. - [9] (./paper.aux) *********** LaTeX2e <2023-06-01> patch level 1 @@ -1175,7 +1175,7 @@ Package logreq Info: Writing requests to 'paper.run.xml'. ) Here is how much of TeX's memory you used: 36963 strings out of 477589 - 757118 string characters out of 5817003 + 757166 string characters out of 5817003 1940432 words of memory out of 5000000 57602 multiletter control sequences out of 15000+600000 564981 words of font info for 89 fonts, out of 8000000 for 9000 diff --git a/papers/JOSE/paper.md b/papers/JOSE/paper.md index c376cb3e2..223b0056b 100644 --- a/papers/JOSE/paper.md +++ b/papers/JOSE/paper.md @@ -121,7 +121,11 @@ Importantly, whatever approach researchers choose remains a subjective decision, Researchers frequently attempt to identify outliers using measures of deviation from the center of a variable's distribution. One of the most popular such procedure is the _z_ score transformation, which computes the distance in standard deviation (SD) from the mean. However, as mentioned earlier, this popular method is not robust. Therefore, for univariate outliers, it is recommended to use the median along with the Median Absolute Deviation (MAD), which are more robust than the interquartile range or the mean and its standard deviation [@leys2019outliers; @leys2013outliers]. -Researchers can identify outliers based on robust (i.e., MAD-based) _z_ scores using the `check_outliers()` function of the *{performance}* package, by specifying `method = "zscore_robust"`.^[Note that `check_outliers()` only checks numeric variables.] Although @leys2013outliers suggest a default threshold of 2.5 and @leys2019outliers a threshold of 3, *{performance}* uses by default a less conservative threshold of ~3.29.^[3.29 is an approximation of the two-tailed critical value for _p_ < .001, obtained through `qnorm(p = 1 - 0.001 / 2)`. We chose this threshold for consistency with the thresholds of all our other methods.] That is, data points will be flagged as outliers if they go beyond +/- ~3.29 MAD. Users can adjust this threshold using the `threshold` argument, as demonstrated below. +Researchers can identify outliers based on robust (i.e., MAD-based) _z_ scores using the `check_outliers()` function of the *{performance}* package, by specifying `method = "zscore_robust"`.^[Note that `check_outliers()` only checks numeric variables.] Although @leys2013outliers suggest a default threshold of 2.5 and @leys2019outliers a threshold of 3, *{performance}* uses by default a less conservative threshold of ~3.29.^[3.29 is an approximation of the two-tailed critical value for _p_ < .001, obtained through `qnorm(p = 1 - 0.001 / 2)`. We chose this threshold for consistency with the thresholds of all our other methods.] That is, data points will be flagged as outliers if they go beyond +/- ~3.29 MAD. Users can adjust this threshold using the `threshold` argument. + +Below we provide example code using the `mtcars` dataset, which was extracted from the 1974 *Motor Trend* US magazine. The dataset contains fuel consumption and 10 characteristics of automobile design and performance for 32 different car models (see `?mtcars` for details). We chose this dataset because it is accessible from base R and familiar to many R users. We might want to conduct specific statistical analyses on this data set, say, _t_ tests or structural equation modelling, but first, we want to check for outliers that may influence those test results. + +Because the automobile names are stored as column names in `mtcars`, we first have to convert them to an ID column to benefit from the `check_outliers()` ID argument. Furthermore, we only really need a couple columns for this demonstration, so we choose the first four (`mpg` = Miles/(US) gallon; `cyl` = Number of cylinders; `disp` = Displacement; `hp` = Gross horsepower). Finally, because there are no outliers in this dataset, we add two artificial outliers before running our function. ```r @@ -163,7 +167,9 @@ outliers #> 34 34 34 16.52502 ``` -The row numbers of the detected outliers can be obtained by using `which()` on the output object, which can be used for exclusions for example: +What we see is that `check_outliers()` with the robust _z_ score method detected two outliers: cases 33 and 34, which were the observations we added ourselves. They were flagged for two variables specifically: `mpg` (Miles/(US) gallon) and `cyl` (Number of cylinders), and the output provides their exact _z_ score for those variables. + +We describe how to deal with those cases in more details later in the paper, but should we want to exclude these detected outliers from the main dataset, we can extract row numbers using `which()` on the output object, which can then be used for indexing: ```r @@ -178,8 +184,6 @@ which(outliers) data_clean <- data[-which(outliers), ] ``` -All `check_outliers()` output objects possess a `plot()` method, meaning it is also possible to visualize the outliers using the generic `plot()` function on the resulting outlier object after loading the {see} package. - Other univariate methods are available, such as using the interquartile range (IQR), or based on different intervals, such as the Highest Density Interval (HDI) or the Bias Corrected and Accelerated Interval (BCI). These methods are documented and described in the function's [help page](). ## Multivariate Outliers @@ -204,6 +208,8 @@ outliers #> - For variables: mpg, cyl, disp, hp. ``` +Here, we detected 9 multivariate outliers (i.e,. when looking at all variables of our dataset together). + Other multivariate methods are available, such as another type of robust Mahalanobis distance that in this case relies on an orthogonalized Gnanadesikan-Kettenring pairwise estimator [@gnanadesikan1972robust]. These methods are documented and described in the function's [help page](https://easystats.github.io/performance/reference/check_outliers.html). ## Model-Based Outliers @@ -225,12 +231,17 @@ outliers #> - For variable: (Whole model). ``` +Using the model-based outlier detection method, we identified a single outlier. + +All `check_outliers()` output objects possess a `plot()` method, meaning it is also possible to visualize the outliers using the generic `plot()` function on the resulting outlier object after loading the {see} package. + + ```r plot(outliers) ``` \begin{figure} -\includegraphics[width=1\linewidth]{paper_files/figure-latex/model-1} \caption{Visual depiction of outliers based on Cook's distance (leverage and standardized residuals), based on the fitted model.}\label{fig:model} +\includegraphics[width=1\linewidth]{paper_files/figure-latex/model_fig-1} \caption{Visual depiction of outliers based on Cook's distance (leverage and standardized residuals), based on the fitted model.}\label{fig:model_fig} \end{figure} Table 1 below summarizes which methods to use in which cases, and with what threshold. diff --git a/papers/JOSE/paper.pdf b/papers/JOSE/paper.pdf index b3503ccf84a60ae284a2efdfc55648de68c0b9d6..96f13be448ff85b629ba1fda602383690df7c596 100644 GIT binary patch delta 64616 zcmZs>Q;;T1xOLfuF59+k+qP}ne#^FP+qPX@wryMUotcS=^G8fxC9ZeIvtqB6RG5@1 z82@IVX+vOE&NRkdAQAvGD>FMEAC$9;lc}LCl*h(3_EaoR$8~O9IlhJFEjUBEaQqcf zhwXuOe2}-77d<2JXX0)gMI=&*(yL0`^#~r?XnU7xqQt#yWQ*_m64@hv%io^Ac_K2K zQ>Q$4&Oe_mz9*Km$L5k7Oxx0i#?fBfoWzMuo01yF2FGE2zNvss{hzMyg_WQ8! z(^itiRliSE`Zh7b#gMBR7Kq!dC>uKY`Q=n zO7(lP_#+Nr)>(i5^RbWr$M^G6TtKberxWnC)$3P7VcF)H5E$XFG%5^=&MYU!Ay1L> z$<{VoScpnj@(y4?Oi-tHU=UhfF+P{Zo4&gFQsG4e1Wcm7|FiOJ2|4cV@1WC-Y)OM^VTN-q1QQY-&vYk7GF-)vDB~@5h?!w$b4rq+GuRY|3%$Zz z|GHy}EK3?DT4ka1N*^H;m{plL7*<6lbE1b#3)KcnXwEr;=vqP{Fc+~-9z9Nc1n*8l zgcrazh67lEZJbG!g!JF5iSSz=j-#vo0M9CHYM zi}zP)&_r1FAPlmE77sCVN>jMbaZz=ajD6}@IF~{pm`pH=b)jSvP?M~&NEBMl2sncQ zuYh4$H}Yn;L?WJ?5F4X@_23V-nV8gjt9 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zfd2cG`&TpbXE#vIO%U+2bqByV?*5~B_~%I$-y{8P;1^`Tw=2Ey%~x++XAuV$G@Ko9 z$KbzC*MA@H1^?_5|C*^_hqgnYoN)f|CjQxe{nOXqphnAC!w_x?z%@*9fAD>1kN{ZZ zPl$sP|Gxb%=t>C04-)1Afw*vb{{>|IsbYwOSnfE;093X^c;WiYzdF3$2!y>I5{buI zhPR!)0JzVu(D;9ahQnThA_5=)_wNw@L|(q0a7Qu_Kv0wn^sfsbDk6gGoI3)3%fLdo zD&j8y^0y2kiU%tHE&~aIaoFiUWFSFY_5NK35ryCY-@nU*h5uOAg0PxLo0N(V^8%2PHq##sYQBF=wQ5Y%;mJ^i+DS|*kq9757k`hP} iA}1&+4fx+GR`@5y3vK6#{<)S=9B?P&;84<0Ci_1iOY(~V literal 0 HcmV?d00001 From 44d11e143ed67645aec02131e34e6c63dcf3e62a Mon Sep 17 00:00:00 2001 From: rempsyc Date: Wed, 4 Oct 2023 15:07:03 -0400 Subject: [PATCH 27/34] addresses #636 major points --- papers/JOSE/paper.Rmd | 8 +++++--- papers/JOSE/paper.log | 14 +++++++++----- papers/JOSE/paper.md | 8 +++++--- papers/JOSE/paper.pdf | Bin 202133 -> 202771 bytes .../paper_files/figure-latex/model_fig-1.pdf | Bin 8480 -> 8479 bytes vignettes/check_outliers.Rmd | 4 +++- 6 files changed, 22 insertions(+), 12 deletions(-) diff --git a/papers/JOSE/paper.Rmd b/papers/JOSE/paper.Rmd index bbd9bcaad..c72fefc15 100644 --- a/papers/JOSE/paper.Rmd +++ b/papers/JOSE/paper.Rmd @@ -29,7 +29,7 @@ affiliations: - index: 1 name: Department of Psychology, Université du Québec à Montréal, Montréal, Québec, Canada - index: 2 - name: Independent Researcher + name: Independent Researcher, Ramat Gan, Israel - index: 3 name: Center for Humans and Machines, Max Planck Institute for Human Development, Berlin, Germany - index: 4 @@ -115,7 +115,7 @@ Nonetheless, the improper handling of these outliers can substantially affect st One possible reason is that researchers are not aware of the existing recommendations, or do not know how to implement them using their analysis software. In this paper, we show how to follow current best practices for automatic and reproducible statistical outlier detection (SOD) using R and the *{performance}* package [@ludecke2021performance], which is part of the *easystats* ecosystem of packages that build an R framework for easy statistical modeling, visualization, and reporting [@easystatspackage]. Installation instructions can be found on [GitHub](https://github.com/easystats/performance) or its [website](https://easystats.github.io/performance/), and its list of dependencies on [CRAN](https://cran.r-project.org/package=performance). -The instructional materials that follow is aimed at an audience of researchers who want to follow good practices, and is appropriate for advanced undergraduate students, graduate students, professors, or professionals having to deal with the nuances of outlier treatment. +The instructional materials that follow are aimed at an audience of researchers who want to follow good practices, and are appropriate for advanced undergraduate students, graduate students, professors, or professionals having to deal with the nuances of outlier treatment. # Identifying Outliers @@ -123,7 +123,7 @@ Although many researchers attempt to identify outliers with measures based on th Nonetheless, which exact outlier method to use depends on many factors. In some cases, eye-gauging odd observations can be an appropriate solution, though many researchers will favour algorithmic solutions to detect potential outliers, for example, based on a continuous value expressing the observation stands out from the others. -One of the factors to consider when selecting an algorithmic outlier detection method is the statistical test of interest. When using a regression model, relevant information can be found by identifying observations that do not fit well with the model. This approach, known as model-based outliers detection (as outliers are extracted after the statistical model has been fit), can be contrasted with distribution-based outliers detection, which is based on the distance between an observation and the "center" of its population. Various quantification strategies of this distance exist for the latter, both univariate (involving only one variable at a time) or multivariate (involving multiple variables). +One of the factors to consider when selecting an algorithmic outlier detection method is the statistical test of interest. Identifying observations the regression model does not fit well can help find information relevant to our specific research context. This approach, known as model-based outliers detection (as outliers are extracted after the statistical model has been fit), can be contrasted with distribution-based outliers detection, which is based on the distance between an observation and the "center" of its population. Various quantification strategies of this distance exist for the latter, both univariate (involving only one variable at a time) or multivariate (involving multiple variables). When no method is readily available to detect model-based outliers, such as for structural equation modelling (SEM), looking for multivariate outliers may be of relevance. For simple tests (_t_ tests or correlations) that compare values of the same variable, it can be appropriate to check for univariate outliers. However, univariate methods can give false positives since _t_ tests and correlations, ultimately, are also models/multivariable statistics. They are in this sense more limited, but we show them nonetheless for educational purposes. @@ -187,6 +187,8 @@ Working with regression models creates the possibility of using model-based SOD In {performance}, two such model-based SOD methods are currently available: Cook's distance, for regular regression models, and Pareto, for Bayesian models. As such, `check_outliers()` can be applied directly on regression model objects, by simply specifying `method = "cook"` (or `method = "pareto"` for Bayesian models).^[Our default threshold for the Cook method is defined by `stats::qf(0.5, ncol(x), nrow(x) - ncol(x))`, which again is an approximation of the critical value for _p_ < .001 consistent with the thresholds of our other methods.] +Currently, most lm models are supported (with the exception of `glmmTMB`, `lmrob`, and `glmrob` models), as long as they are supported by the underlying functions `stats::cooks.distance()` (or `loo::pareto_k_values()`) and `insight::get_data()` (for a full list of the 225 models currently supported by the `insight` package, see https://easystats.github.io/insight/#list-of-supported-models-by-class). We show a demo below. + ```{r model} model <- lm(disp ~ mpg * disp, data = data) outliers <- check_outliers(model, method = "cook") diff --git a/papers/JOSE/paper.log b/papers/JOSE/paper.log index b1a43ab5f..33daaa7f8 100644 --- a/papers/JOSE/paper.log +++ b/papers/JOSE/paper.log @@ -1,4 +1,4 @@ -This is XeTeX, Version 3.141592653-2.6-0.999995 (TeX Live 2023) (preloaded format=xelatex 2023.9.14) 4 OCT 2023 11:22 +This is XeTeX, Version 3.141592653-2.6-0.999995 (TeX Live 2023) (preloaded format=xelatex 2023.9.14) 4 OCT 2023 15:06 entering extended mode restricted \write18 enabled. %&-line parsing enabled. @@ -1097,6 +1097,10 @@ Package fancyhdr Warning: \headheight is too small (62.59596pt): (fancyhdr) \addtolength{\topmargin}{-1.71957pt}. [4] +Underfull \hbox (badness 1331) in paragraph at lines 627--635 +[][]$[][][][][] [] [] [] [][][][][][][][][] [] [][][][][][] [] [][] [] [][][][][][][] [] [][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][]$[][]\TU/lmr/m/n/10 ). We show a + [] + File: paper_files/figure-latex/model_fig-1.pdf Graphic file (type pdf) File: D:/Rpackages/rticles/rmarkdown/templates/joss/resources/JOSE-logo.png Graphic file (type bmp) @@ -1139,17 +1143,17 @@ Package fancyhdr Warning: \headheight is too small (62.59596pt): (fancyhdr) \addtolength{\topmargin}{-1.71957pt}. [8] -Underfull \hbox (badness 1584) in paragraph at lines 959--965 +Underfull \hbox (badness 1584) in paragraph at lines 968--974 []\TU/lmr/m/n/10 Simmons, J. P., Nelson, L. D., & Simonsohn, U. (2011). False-positive psy- [] -Underfull \hbox (badness 3049) in paragraph at lines 959--965 +Underfull \hbox (badness 3049) in paragraph at lines 968--974 \TU/lmr/m/n/10 chology: Undisclosed flexibility in data collection and analysis allows pre- [] -Underfull \hbox (badness 3735) in paragraph at lines 959--965 +Underfull \hbox (badness 3735) in paragraph at lines 968--974 \TU/lmr/m/n/10 senting anything as significant. \TU/lmr/m/it/10 Psychological Science\TU/lmr/m/n/10 , \TU/lmr/m/it/10 22\TU/lmr/m/n/10 (11), 1359–1366. [] @@ -1180,6 +1184,6 @@ Here is how much of TeX's memory you used: 57602 multiletter control sequences out of 15000+600000 564981 words of font info for 89 fonts, out of 8000000 for 9000 14 hyphenation exceptions out of 8191 - 84i,12n,87p,1194b,850s stack positions out of 10000i,1000n,20000p,200000b,200000s + 84i,13n,87p,1194b,850s stack positions out of 10000i,1000n,20000p,200000b,200000s Output written on paper.pdf (9 pages). diff --git a/papers/JOSE/paper.md b/papers/JOSE/paper.md index 223b0056b..ef0dd7007 100644 --- a/papers/JOSE/paper.md +++ b/papers/JOSE/paper.md @@ -29,7 +29,7 @@ affiliations: - index: 1 name: Department of Psychology, Université du Québec à Montréal, Montréal, Québec, Canada - index: 2 - name: Independent Researcher + name: Independent Researcher, Ramat Gan, Israel - index: 3 name: Center for Humans and Machines, Max Planck Institute for Human Development, Berlin, Germany - index: 4 @@ -103,7 +103,7 @@ Nonetheless, the improper handling of these outliers can substantially affect st One possible reason is that researchers are not aware of the existing recommendations, or do not know how to implement them using their analysis software. In this paper, we show how to follow current best practices for automatic and reproducible statistical outlier detection (SOD) using R and the *{performance}* package [@ludecke2021performance], which is part of the *easystats* ecosystem of packages that build an R framework for easy statistical modeling, visualization, and reporting [@easystatspackage]. Installation instructions can be found on [GitHub](https://github.com/easystats/performance) or its [website](https://easystats.github.io/performance/), and its list of dependencies on [CRAN](https://cran.r-project.org/package=performance). -The instructional materials that follow is aimed at an audience of researchers who want to follow good practices, and is appropriate for advanced undergraduate students, graduate students, professors, or professionals having to deal with the nuances of outlier treatment. +The instructional materials that follow are aimed at an audience of researchers who want to follow good practices, and are appropriate for advanced undergraduate students, graduate students, professors, or professionals having to deal with the nuances of outlier treatment. # Identifying Outliers @@ -111,7 +111,7 @@ Although many researchers attempt to identify outliers with measures based on th Nonetheless, which exact outlier method to use depends on many factors. In some cases, eye-gauging odd observations can be an appropriate solution, though many researchers will favour algorithmic solutions to detect potential outliers, for example, based on a continuous value expressing the observation stands out from the others. -One of the factors to consider when selecting an algorithmic outlier detection method is the statistical test of interest. When using a regression model, relevant information can be found by identifying observations that do not fit well with the model. This approach, known as model-based outliers detection (as outliers are extracted after the statistical model has been fit), can be contrasted with distribution-based outliers detection, which is based on the distance between an observation and the "center" of its population. Various quantification strategies of this distance exist for the latter, both univariate (involving only one variable at a time) or multivariate (involving multiple variables). +One of the factors to consider when selecting an algorithmic outlier detection method is the statistical test of interest. Identifying observations the regression model does not fit well can help find information relevant to our specific research context. This approach, known as model-based outliers detection (as outliers are extracted after the statistical model has been fit), can be contrasted with distribution-based outliers detection, which is based on the distance between an observation and the "center" of its population. Various quantification strategies of this distance exist for the latter, both univariate (involving only one variable at a time) or multivariate (involving multiple variables). When no method is readily available to detect model-based outliers, such as for structural equation modelling (SEM), looking for multivariate outliers may be of relevance. For simple tests (_t_ tests or correlations) that compare values of the same variable, it can be appropriate to check for univariate outliers. However, univariate methods can give false positives since _t_ tests and correlations, ultimately, are also models/multivariable statistics. They are in this sense more limited, but we show them nonetheless for educational purposes. @@ -218,6 +218,8 @@ Working with regression models creates the possibility of using model-based SOD In {performance}, two such model-based SOD methods are currently available: Cook's distance, for regular regression models, and Pareto, for Bayesian models. As such, `check_outliers()` can be applied directly on regression model objects, by simply specifying `method = "cook"` (or `method = "pareto"` for Bayesian models).^[Our default threshold for the Cook method is defined by `stats::qf(0.5, ncol(x), nrow(x) - ncol(x))`, which again is an approximation of the critical value for _p_ < .001 consistent with the thresholds of our other methods.] +Currently, most lm models are supported (with the exception of `glmmTMB`, `lmrob`, and `glmrob` models), as long as they are supported by the underlying functions `stats::cooks.distance()` (or `loo::pareto_k_values()`) and `insight::get_data()` (for a full list of the 225 models currently supported by the `insight` package, see https://easystats.github.io/insight/#list-of-supported-models-by-class). We show a demo below. + ```r model <- lm(disp ~ mpg * disp, data = data) diff --git a/papers/JOSE/paper.pdf b/papers/JOSE/paper.pdf index 96f13be448ff85b629ba1fda602383690df7c596..f6cbe4b67940b2a57957a04cb78461e1c10a3bb9 100644 GIT binary patch delta 60028 zcmZU)V{j#G(5@TXwvCBx+jcUsZLHX~?PSHa?Mysbu`zKbnB=_QIlE5nUHjkDb^pDp z`l;@|GU|}hnvjCqz>!4&+^oXF2<{$kmS&C!KHE1$vx!uE_X|45sG1GLK?)VZWV%qD z5h=W6C`P*)F4=lexIv@>*Dm1&w|>`5va)qK>N=L&2Te!+rhb2QUnrdb{1BUn-rISIl|a{WDk#xZ(NU4B{Qi{{DJj zec65WTQ!3%AP?wqn!a7O)+N7@pS)T9Fj4}Y^oRL}e~L{57B`Sge%WR1uMFvr*zI(#kbS6OK9pkwTzb{5gGnmtxKeCht&E1{jx_@ax?Y_%P`s?Wfv^v?3u zpUoxn?P4JSE+!2nbg~5)93TB&1L$a4*L1ng`*<0_JTN)>TlKx}&0g9 z{#)+Hf5ATkaHRO9yJkkEs95T)RE>;kv+=U^a#7gpSjzIa@1nV5K@gsVugTKC`md@d zg?y9rDK#|y@EgFp2>jK1NyW?lG;Ibs}-p@A|U9+_~Xh?z)szlz@H2p;@OJZtsN>ju^_f6Txub`V`C{+5?8rVNx= zST5`C_G(wQ5#o7(fpEj?W8W*5uf05%6*m7zlEYvGSrIbUa6txSpG<91Sks`VUrOQ0 zj<2)@1g>s2ZfE00C;XL^r9i}7;M%ogDIbO_L^r^ut<4*^<6o9_q(v3Aj+zob#PsFj??+x=Ahg`>Y*VdW_T6Xrm+RrbQr}U%@4-dt)KIGo#^D8(j zz>hKJfD#skf5%=~;gMeU$OST%5<)AzV3s?ZUPd{N^MfLtYC^1ME9w3S4r8{k0*p|x z(2ApRLhWx%H!CX3G`ByZOsa&a55jo0_@F?%`D*@N3mqa~4S;_edxd@cP~s5q_Fg99 zwqS$yRnP^ODf?z6RXD|dcGS^JRNOA802zF*s}M0wl$*FLtLKJPd&I$r9WeBzA)Bo- z4g! z^!7Ee!zAJg>j~rN`)L$)st4FZ!8=|3yV~(D_+e_UkyGl`Pl`JAX2))!K{2ag}$s;(4=hawo z7A=K1x+N-aqEWsfXut&xyAWNIf{50S#-aS&`zPiDV?gzD6OtCqc3bQRz`N|a%`4Hv zZX{`B4u|xG$~3XDWM>$IzRiR=mq5JB6@uE`A7XG#qFClP*S9G7G(*#nQT7#j!bDOoQtFKk(RmlYPMxIKKtu-}?dxrn@RJ zhbSFmT}DwDT2)5)j1NI48tlZ>WXQKMHj3h}!E(>=eUG}?Db)k*wgY{m@yeqPlVmP2#K|T7mbN_bfa&L@J$-y+OvJDZ0IQ5Ylfk%JgaQ*< zswU}{J$}%^Ac{dV8{t@=9{2{jr9;19l(%rlX&A|m&3j{j7pSQ2n$XZ;@h$AZuv$LK zNfUb3cDRhhm}+5C{EVVFsvu!aFVxPrJW3dUHZ$&?(&Ml-GHeo+lz$D3ML-Cac<(YM zueo8crK^p`#A{&#d|qki=ym=^_3=FQU@;H%I+}UXjp2A&LAb0!T&>meK_5+JspVZx z(N7^i{1>+Lvw*XOTL$XfdKF%EZAR)2>jZ+OOdO+Th1xZEHP8qR1$JP?RnI+w93A)C zf$I``+>@kc;Eal9yK;XaKnHJg=3I9rRDaEb4)Tid3`cX(!ygty?WzVRk~C5BDj%YCK^RIrxN} z+&@z0WsJ}e=iQkiafN5msWyHcl2`_BUgzCtYGXhFXqgZ0DaIa;0(mX5phv?Sol}|A zFcOH7_;~_N^7D|e;+Q;LH7Qr|x(N9q_en!pB}siov~1yk$|Z1q^3su%yui$0t>2E( zm?1?e$kAVwMWU2`aB100QJdg0ATF(Q7b+flegUS}_y`9Mf_f5;5#0xI9T=ULRdi%+ zNx5vmgKqiEJ~14B!!KG}5vcUU_le7>1pfiP`>r*w16Fd8fmZlN1qXs8oN0?EDqc=Lz!PfEB_H}oDT*lG)jMz_Rb)F^z&ZAvGNMI!shNu@U>|U znP=f>sXk1I=jf`4P>Q&&4b$eC_^jCk=X*UzrbJ zjif}YuVQEIhf+h8gTpQVb5F|w+V4W#^A21gC`xgyi=eTJ`yaL-VUw9mQD3(a81Gtq zE)9O>vcd%YG)eo@>=^=D2oVbLetucV8W+3jTzb`C4x)Q;@0s|51p~OYwH;8ll#+Am zoNRMH!(npQ6s%f=o*DjZ!0W_9o>rm(67q}!k223zacKhi@`My;!? zE$g@^DLrJbf0(TmFo`9qrD=Bkjnn1nd(GqnvP{BF7rQ#}wK|fc)NJzl(I>aWj_Fe2TXdNznRv z2NJekbT144OM>Ea)PdQfC1i z%G$=Ty6T#_n8r@D4SG4BYIdqRv-`L6luxs3oAd@O4`<4YW9I_wD{va8E9B_v!z&J! zZ9&ZSgXb>{QJzwbD*gR?Px?-yjP4lQ3y2cC+bFYrz@ZD#2UH|X^Il+oc45eogYb=F0npv?rW)W zh}NyE{hWTL8c)yHA0b9@r?f0T!fyyn);YnYj^+@Px%nrl-g2pER?pVj7#*h6o<}3q z9&W~wKiK}3;3_;tu~qI{iE)c&ABX&E6+hqz9BDRLy3huwjY*#D6|8-FFgFmPvbkG^u6CO#D5Cy1xsgksil!_M^+UlJ!+xVU^OwucSiO zcvFas2}jA_4qPF%_#j+e0`|pQ_I^HZPlsZ%h#?{If~Y<6xJb% z7<{|slRL&-y70ovHgrqS08 zR)8)>=YQ7O_#FicMtf1SFd?tGYD?!>CxO3Iuj91mnzwyd-$mz3{E5zss4AuE=Qkkv z`&=f9tM+Piz`F97uckMc4t~L^U|s0~mEu{%0`7`WX?@KQ$_64jxCvqX$zZ(H zO?Ci?k)T`BB;+@Na!93%cDm&o9L2cgV5|%}M)09D_GK+RA_8KwcqRM71Zk3)7_K$I zs6A9L{aj75U*HWz4~vfj!9@S8i6(ugi{dd@_Q3(zU-)6e0&G!E)nN1*MfnCvyUd$; 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-\usepackage{hyperref} % hyperlinks -\usepackage{url} % simple URL typesetting -\usepackage{booktabs} % professional-quality tables -\usepackage{amsfonts} % blackboard math symbols -\usepackage{nicefrac} % compact symbols for 1/2, etc. -\usepackage{microtype} % microtypography -\usepackage{graphicx} - -\title{Check your outliers! An introduction to identifying statistical -outliers in R with \emph{easystats}} - -\author{ - } - -% Pandoc syntax highlighting -\usepackage{color} -\usepackage{fancyvrb} -\newcommand{\VerbBar}{|} -\newcommand{\VERB}{\Verb[commandchars=\\\{\}]} -\DefineVerbatimEnvironment{Highlighting}{Verbatim}{commandchars=\\\{\}} -% Add ',fontsize=\small' for more characters per line -\usepackage{framed} -\definecolor{shadecolor}{RGB}{248,248,248} -\newenvironment{Shaded}{\begin{snugshade}}{\end{snugshade}} -\newcommand{\AlertTok}[1]{\textcolor[rgb]{0.94,0.16,0.16}{#1}} -\newcommand{\AnnotationTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textbf{\textit{#1}}}} -\newcommand{\AttributeTok}[1]{\textcolor[rgb]{0.77,0.63,0.00}{#1}} -\newcommand{\BaseNTok}[1]{\textcolor[rgb]{0.00,0.00,0.81}{#1}} -\newcommand{\BuiltInTok}[1]{#1} -\newcommand{\CharTok}[1]{\textcolor[rgb]{0.31,0.60,0.02}{#1}} -\newcommand{\CommentTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textit{#1}}} -\newcommand{\CommentVarTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textbf{\textit{#1}}}} -\newcommand{\ConstantTok}[1]{\textcolor[rgb]{0.00,0.00,0.00}{#1}} -\newcommand{\ControlFlowTok}[1]{\textcolor[rgb]{0.13,0.29,0.53}{\textbf{#1}}} -\newcommand{\DataTypeTok}[1]{\textcolor[rgb]{0.13,0.29,0.53}{#1}} -\newcommand{\DecValTok}[1]{\textcolor[rgb]{0.00,0.00,0.81}{#1}} -\newcommand{\DocumentationTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textbf{\textit{#1}}}} -\newcommand{\ErrorTok}[1]{\textcolor[rgb]{0.64,0.00,0.00}{\textbf{#1}}} -\newcommand{\ExtensionTok}[1]{#1} -\newcommand{\FloatTok}[1]{\textcolor[rgb]{0.00,0.00,0.81}{#1}} -\newcommand{\FunctionTok}[1]{\textcolor[rgb]{0.00,0.00,0.00}{#1}} -\newcommand{\ImportTok}[1]{#1} -\newcommand{\InformationTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textbf{\textit{#1}}}} -\newcommand{\KeywordTok}[1]{\textcolor[rgb]{0.13,0.29,0.53}{\textbf{#1}}} -\newcommand{\NormalTok}[1]{#1} -\newcommand{\OperatorTok}[1]{\textcolor[rgb]{0.81,0.36,0.00}{\textbf{#1}}} -\newcommand{\OtherTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{#1}} -\newcommand{\PreprocessorTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textit{#1}}} -\newcommand{\RegionMarkerTok}[1]{#1} -\newcommand{\SpecialCharTok}[1]{\textcolor[rgb]{0.00,0.00,0.00}{#1}} -\newcommand{\SpecialStringTok}[1]{\textcolor[rgb]{0.31,0.60,0.02}{#1}} -\newcommand{\StringTok}[1]{\textcolor[rgb]{0.31,0.60,0.02}{#1}} -\newcommand{\VariableTok}[1]{\textcolor[rgb]{0.00,0.00,0.00}{#1}} -\newcommand{\VerbatimStringTok}[1]{\textcolor[rgb]{0.31,0.60,0.02}{#1}} -\newcommand{\WarningTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textbf{\textit{#1}}}} - -% tightlist command for lists without linebreak -\providecommand{\tightlist}{% - \setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}} - -% From pandoc table feature -\usepackage{longtable,booktabs,array} -\usepackage{calc} % for calculating minipage widths -% Correct order of tables after \paragraph or \subparagraph -\usepackage{etoolbox} -\makeatletter -\patchcmd\longtable{\par}{\if@noskipsec\mbox{}\fi\par}{}{} -\makeatother -% Allow footnotes in longtable head/foot -\IfFileExists{footnotehyper.sty}{\usepackage{footnotehyper}}{\usepackage{footnote}} -\makesavenoteenv{longtable} - -% Pandoc citation processing -\newlength{\cslhangindent} -\setlength{\cslhangindent}{1.5em} -\newlength{\csllabelwidth} -\setlength{\csllabelwidth}{3em} -\newlength{\cslentryspacingunit} % times entry-spacing -\setlength{\cslentryspacingunit}{\parskip} -% for Pandoc 2.8 to 2.10.1 -\newenvironment{cslreferences}% - {}% - {\par} -% For Pandoc 2.11+ -\newenvironment{CSLReferences}[2] % #1 hanging-ident, #2 entry spacing - {% don't indent paragraphs - \setlength{\parindent}{0pt} - % turn on hanging indent if param 1 is 1 - \ifodd #1 - \let\oldpar\par - \def\par{\hangindent=\cslhangindent\oldpar} - \fi - % set entry spacing - \setlength{\parskip}{#2\cslentryspacingunit} - }% - {} -\usepackage{calc} -\newcommand{\CSLBlock}[1]{#1\hfill\break} -\newcommand{\CSLLeftMargin}[1]{\parbox[t]{\csllabelwidth}{#1}} -\newcommand{\CSLRightInline}[1]{\parbox[t]{\linewidth - \csllabelwidth}{#1}\break} -\newcommand{\CSLIndent}[1]{\hspace{\cslhangindent}#1} - -\begin{document} -\maketitle - - -\begin{abstract} -Beyond the challenge of keeping up-to-date with current best practices -regarding the diagnosis and treatment of outliers, an additional -difficulty arises concerning the mathematical implementation of the -recommended methods. In this paper, we provide an overview of current -recommendations and best practices and demonstrate how they can easily -and conveniently be implemented in the R statistical computing software, -using the \emph{\{performance\}} package of the \emph{easystats} -ecosystem. We cover univariate, multivariate, and model-based -statistical outlier detection methods, their recommended threshold, -standard output, and plotting methods. We conclude with recommendations -on the handling of outliers: the different theoretical types of -outliers, whether to exclude or winsorize them, and the importance of -transparency. -\end{abstract} - -\keywords{ - univariate outliers; multivariate outliers; robust detection - methods; R; easystats - } - -\hypertarget{introduction}{% -\section{Introduction}\label{introduction}} - -Real-life data often contain observations that can be considered -\emph{abnormal} when compared to the main population. The cause of -it---be it because they belong to a different distribution (originating -from a different generative process) or simply being extreme cases, -statistically rare but not impossible---can be hard to assess, and the -boundaries of ``abnormal'' difficult to define. - -Nonetheless, the improper handling of these outliers can substantially -affect statistical model estimations, biasing effect estimations and -weakening the models' predictive performance. It is thus essential to -address this problem in a thoughtful manner. Yet, despite the existence -of established recommendations and guidelines, many researchers still do -not treat outliers in a consistent manner, or do so using inappropriate -strategies (Leys et al., 2013; Simmons et al., 2011). - -One possible reason is that researchers are not aware of the existing -recommendations, or do not know how to implement them using their -analysis software. In this paper, we show how to follow current best -practices for automatic and reproducible statistical outlier detection -(SOD) using R and the \emph{\{performance\}} package (Lüdecke et al., -2021), which is part of the \emph{easystats} ecosystem of packages that -build an R framework for easy statistical modeling, visualization, and -reporting (Lüdecke et al., 2019/2023). - -\hypertarget{identifying-outliers}{% -\section{Identifying Outliers}\label{identifying-outliers}} - -Although many researchers attempt to identify outliers with measures -based on the mean (e.g., \emph{z} scores), those methods are problematic -because the mean and standard deviation themselves are not robust to the -influence of outliers and they assume normally distributed data (i.e., a -Gaussian distribution). Therefore, current guidelines recommend using -robust methods to identify outliers, such as those relying on the median -as opposed to the mean (Leys et al., 2013, 2018, 2019). - -Nonetheless, which exact outlier method to use depends on many factors. -In some cases, eye-gauging odd observations can be an appropriate -solution, though many researchers will favour algorithmic solutions to -detect potential outliers, for example, based on a continuous value -expressing the observation stands out from the others. - -One of the factors to consider when selecting an algorithmic outlier -detection method is the statistical test of interest. When using a -regression model, relevant information can be found by identifying -observations that do not fit well with the model. This approach, known -as model-based outliers detection (as outliers are extracted after the -statistical model has been fit), can be contrasted with -distribution-based outliers detection, which is based on the distance -between an observation and the ``center'' of its population. Various -quantification strategies of this distance exist for the latter, both -univariate (involving only one variable at a time) or multivariate -(involving multiple variables). - -When no method is readily available to detect model-based outliers, such -as for structural equation modelling (SEM), looking for multivariate -outliers may be of relevance. For simple tests (\emph{t} tests or -correlations) that compare values of the same variable, it can be -appropriate to check for univariate outliers. However, univariate -methods can give false positives since \emph{t} tests and correlations, -ultimately, are also models/multivariable statistics. They are in this -sense more limited, but we show them nonetheless for educational -purposes. - -Importantly, whatever approach researchers choose remains a subjective -decision, which usage (and rationale) must be transparently documented -and reproducible (Leys et al., 2019). Researchers should commit (ideally -in a preregistration) to an outlier treatment method before collecting -the data. They should report in the paper their decisions and details of -their methods, as well as any deviation from their original plan. These -transparency practices can help reduce false positives due to excessive -researchers' degrees of freedom (i.e., choice flexibility throughout the -analysis). In the following section, we will go through each of the -mentioned methods and provide examples on how to implement them with R. - -\hypertarget{univariate-outliers}{% -\subsection{Univariate Outliers}\label{univariate-outliers}} - -Researchers frequently attempt to identify outliers using measures of -deviation from the center of a variable's distribution. One of the most -popular such procedure is the \emph{z} score transformation, which -computes the distance in standard deviation (SD) from the mean. However, -as mentioned earlier, this popular method is not robust. Therefore, for -univariate outliers, it is recommended to use the median along with the -Median Absolute Deviation (MAD), which are more robust than the -interquartile range or the mean and its standard deviation (Leys et al., -2013, 2019). - -Researchers can identify outliers based on robust (i.e., MAD-based) -\emph{z} scores using the \texttt{check\_outliers()} function of the -\emph{\{performance\}} package, by specifying -\texttt{method\ =\ "zscore\_robust"}.\footnote{Note that - \texttt{check\_outliers()} only checks numeric variables.} Although -Leys et al. (2013) suggest a default threshold of 2.5 and Leys et al. -(2019) a threshold of 3, \emph{\{performance\}} uses by default a less -conservative threshold of \textasciitilde3.29.\footnote{3.29 is an - approximation of the two-tailed critical value for \emph{p} - \textless{} .001, obtained through - \texttt{qnorm(p\ =\ 1\ -\ 0.001\ /\ 2)}. We chose this threshold for - consistency with the thresholds of all our other methods.} That is, -data points will be flagged as outliers if they go beyond +/- -\textasciitilde3.29 MAD. Users can adjust this threshold using the -\texttt{threshold} argument, as demonstrated below. - -\begin{Shaded} -\begin{Highlighting}[] -\FunctionTok{library}\NormalTok{(performance)} - -\CommentTok{\# Create some artificial outliers and an ID column} -\NormalTok{data }\OtherTok{\textless{}{-}} \FunctionTok{rbind}\NormalTok{(mtcars[}\DecValTok{1}\SpecialCharTok{:}\DecValTok{4}\NormalTok{], }\DecValTok{42}\NormalTok{, }\DecValTok{55}\NormalTok{)} -\NormalTok{data }\OtherTok{\textless{}{-}} \FunctionTok{cbind}\NormalTok{(}\AttributeTok{car =} \FunctionTok{row.names}\NormalTok{(data), data)} - -\NormalTok{outliers }\OtherTok{\textless{}{-}} \FunctionTok{check\_outliers}\NormalTok{(data, }\AttributeTok{method =} \StringTok{"zscore\_robust"}\NormalTok{, }\AttributeTok{ID =} \StringTok{"car"}\NormalTok{)} -\NormalTok{outliers} -\end{Highlighting} -\end{Shaded} - -\begin{verbatim} -#> 2 outliers detected: cases 33, 34. -#> - Based on the following method and threshold: zscore_robust (3.291). -#> - For variables: mpg, cyl, disp, hp. -#> -#> ----------------------------------------------------------------------------- -#> -#> The following observations were considered outliers for two or more -#> variables by at least one of the selected methods: -#> -#> Row car n_Zscore_robust -#> 1 33 33 2 -#> 2 34 34 2 -#> -#> ----------------------------------------------------------------------------- -#> Outliers per variable (zscore_robust): -#> -#> $mpg -#> Row car Distance_Zscore_robust -#> 33 33 33 3.709699 -#> 34 34 34 5.848328 -#> -#> $cyl -#> Row car Distance_Zscore_robust -#> 33 33 33 12.14083 -#> 34 34 34 16.52502 -\end{verbatim} - -The row numbers of the detected outliers can be obtained by using -\texttt{which()} on the output object, which can be used for exclusions -for example: - -\begin{Shaded} -\begin{Highlighting}[] -\FunctionTok{which}\NormalTok{(outliers)} -\end{Highlighting} -\end{Shaded} - -\begin{verbatim} -#> [1] 33 34 -\end{verbatim} - -\begin{Shaded} -\begin{Highlighting}[] -\NormalTok{data\_clean }\OtherTok{\textless{}{-}}\NormalTok{ data[}\SpecialCharTok{{-}}\FunctionTok{which}\NormalTok{(outliers), ]} -\end{Highlighting} -\end{Shaded} - -All \texttt{check\_outliers()} output objects possess a \texttt{plot()} -method, meaning it is also possible to visualize the outliers: - -\begin{Shaded} -\begin{Highlighting}[] -\FunctionTok{library}\NormalTok{(see)} - -\FunctionTok{plot}\NormalTok{(outliers)} -\end{Highlighting} -\end{Shaded} - -\begin{figure} -\includegraphics[width=1\linewidth]{paper_files/figure-latex/univariate_implicit-1} \caption{Visual depiction of outliers using the robust z-score method. The distance represents an aggregate score for variables mpg, cyl, disp, and hp.}\label{fig:univariate_implicit} -\end{figure} - -Other univariate methods are available, such as using the interquartile -range (IQR), or based on different intervals, such as the Highest -Density Interval (HDI) or the Bias Corrected and Accelerated Interval -(BCI). These methods are documented and described in the function's -\href{https://easystats.github.io/performance/reference/check_outliers.html}{help -page}. - -\hypertarget{multivariate-outliers}{% -\subsection{Multivariate Outliers}\label{multivariate-outliers}} - -Univariate outliers can be useful when the focus is on a particular -variable, for instance the reaction time, as extreme values might be -indicative of inattention or non-task-related behavior\footnote{ Note - that they might not be the optimal way of treating reaction time - outliers (Ratcliff, 1993; Van Zandt \& Ratcliff, 1995)}. - -However, in many scenarios, variables of a data set are not independent, -and an abnormal observation will impact multiple dimensions. For -instance, a participant giving random answers to a questionnaire. In -this case, computing the \emph{z} score for each of the questions might -not lead to satisfactory results. Instead, one might want to look at -these variables together. - -One common approach for this is to compute multivariate distance metrics -such as the Mahalanobis distance. Although the Mahalanobis distance is -very popular, just like the regular \emph{z} scores method, it is not -robust and is heavily influenced by the outliers themselves. Therefore, -for multivariate outliers, it is recommended to use the Minimum -Covariance Determinant, a robust version of the Mahalanobis distance -(MCD, Leys et al., 2018, 2019). - -In \emph{\{performance\}}'s \texttt{check\_outliers()}, one can use this -approach with \texttt{method\ =\ "mcd"}.\footnote{Our default threshold - for the MCD method is defined by - \texttt{stats::qchisq(p\ =\ 1\ -\ 0.001,\ df\ =\ ncol(x))}, which - again is an approximation of the critical value for \emph{p} - \textless{} .001 consistent with the thresholds of our other methods.} - -\begin{Shaded} -\begin{Highlighting}[] -\NormalTok{outliers }\OtherTok{\textless{}{-}} \FunctionTok{check\_outliers}\NormalTok{(data, }\AttributeTok{method =} \StringTok{"mcd"}\NormalTok{)} -\NormalTok{outliers} -\end{Highlighting} -\end{Shaded} - -\begin{verbatim} -#> 9 outliers detected: cases 7, 15, 16, 17, 24, 29, 31, 33, 34. -#> - Based on the following method and threshold: mcd (20). -#> - For variables: mpg, cyl, disp, hp. -\end{verbatim} - -\begin{Shaded} -\begin{Highlighting}[] -\FunctionTok{plot}\NormalTok{(outliers)} -\end{Highlighting} -\end{Shaded} - -\begin{figure} -\includegraphics[width=1\linewidth]{paper_files/figure-latex/multivariate_implicit-1} \caption{Visual depiction of outliers using the Minimum Covariance Determinant (MCD) method, a robust version of the Mahalanobis distance. The distance represents the MCD scores for variables mpg, cyl, disp, and hp.}\label{fig:multivariate_implicit} -\end{figure} - -Other multivariate methods are available, such as another type of robust -Mahalanobis distance that in this case relies on an orthogonalized -Gnanadesikan-Kettenring pairwise estimator (Gnanadesikan \& Kettenring, -1972). These methods are documented and described in the function's -\href{https://easystats.github.io/performance/reference/check_outliers.html}{help -page}. - -\hypertarget{model-based-outliers}{% -\subsection{Model-Based Outliers}\label{model-based-outliers}} - -Working with regression models creates the possibility of using -model-based SOD methods. These methods rely on the concept of -\emph{leverage}, that is, how much influence a given observation can -have on the model estimates. If few observations have a relatively -strong leverage/influence on the model, one can suspect that the model's -estimates are biased by these observations, in which case flagging them -as outliers could prove helpful (see next section, ``Handling -Outliers''). - -In \{performance\}, two such model-based SOD methods are currently -available: Cook's distance, for regular regression models, and Pareto, -for Bayesian models. As such, \texttt{check\_outliers()} can be applied -directly on regression model objects, by simply specifying -\texttt{method\ =\ "cook"} (or \texttt{method\ =\ "pareto"} for Bayesian -models).\footnote{Our default threshold for the Cook method is defined - by \texttt{stats::qf(0.5,\ ncol(x),\ nrow(x)\ -\ ncol(x))}, which - again is an approximation of the critical value for \emph{p} - \textless{} .001 consistent with the thresholds of our other methods.} - -\begin{Shaded} -\begin{Highlighting}[] -\NormalTok{model }\OtherTok{\textless{}{-}} \FunctionTok{lm}\NormalTok{(disp }\SpecialCharTok{\textasciitilde{}}\NormalTok{ mpg }\SpecialCharTok{*}\NormalTok{ disp, }\AttributeTok{data =}\NormalTok{ data)} -\NormalTok{outliers }\OtherTok{\textless{}{-}} \FunctionTok{check\_outliers}\NormalTok{(model, }\AttributeTok{method =} \StringTok{"cook"}\NormalTok{)} -\NormalTok{outliers} -\end{Highlighting} -\end{Shaded} - -\begin{verbatim} -#> 1 outlier detected: case 34. -#> - Based on the following method and threshold: cook (0.708). -#> - For variable: (Whole model). -\end{verbatim} - -\begin{Shaded} -\begin{Highlighting}[] -\FunctionTok{plot}\NormalTok{(outliers)} -\end{Highlighting} -\end{Shaded} - -\begin{figure} -\includegraphics[width=1\linewidth]{paper_files/figure-latex/model-1} \caption{Visual depiction of outliers based on Cook's distance (leverage and standardized residuals), based on the fitted model.}\label{fig:model} -\end{figure} - -Table 1 below summarizes which methods to use in which cases, and with -what threshold. - -\begin{longtable}[]{@{} - >{\raggedright\arraybackslash}p{(\columnwidth - 4\tabcolsep) * \real{0.3506}} - >{\raggedright\arraybackslash}p{(\columnwidth - 4\tabcolsep) * \real{0.3161}} - >{\raggedright\arraybackslash}p{(\columnwidth - 4\tabcolsep) * \real{0.3333}}@{}} -\caption{Summary of Statistical Outlier Detection Methods -Recommendations.}\tabularnewline -\toprule() -\begin{minipage}[b]{\linewidth}\raggedright -Statistical Test -\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedright -Diagnosis Method -\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedright -Recommended Threshold -\end{minipage} \\ -\midrule() -\endfirsthead -\toprule() -\begin{minipage}[b]{\linewidth}\raggedright -Statistical Test -\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedright -Diagnosis Method -\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedright -Recommended Threshold -\end{minipage} \\ -\midrule() -\endhead -Supported regression model & \textbf{Model-based}: Cook (or Pareto for -Bayesian models) & \texttt{qf(0.5,\ ncol(x),\ nrow(x)\ -\ ncol(x))} (or -0.7 for Pareto) \\ -Structural Equation Modeling (or other unsupported model) & -\textbf{Multivariate}: Minimum Covariance Determinant (MCD) & -\texttt{qchisq(p\ =\ 1\ -\ 0.001,\ df\ =\ ncol(x))} \\ -Simple test with few variables (\emph{t} test, correlation, etc.) & -\textbf{Univariate}: robust \emph{z} scores (MAD) & -\texttt{qnorm(p\ =\ 1\ -\ 0.001\ /\ 2)}, \textasciitilde{} 3.29 \\ -\bottomrule() -\end{longtable} - -\hypertarget{cooks-distance-vs.-mcd}{% -\subsection{Cook's Distance vs.~MCD}\label{cooks-distance-vs.-mcd}} - -Leys et al. (2018) report a preference for the MCD method over Cook's -distance. This is because Cook's distance removes one observation at a -time and checks its corresponding influence on the model each time -(Cook, 1977), and flags any observation that has a large influence. In -the view of these authors, when there are several outliers, the process -of removing a single outlier at a time is problematic as the model -remains ``contaminated'' or influenced by other possible outliers in the -model, rendering this method suboptimal in the presence of multiple -outliers. - -However, distribution-based approaches are not a silver bullet either, -and there are cases where the usage of methods agnostic to theoretical -and statistical models of interest might be problematic. For example, a -very tall person would be expected to also be much heavier than average, -but that would still fit with the expected association between height -and weight (i.e., it would be in line with a model such as -\texttt{weight\ \textasciitilde{}\ height}). In contrast, using -multivariate outlier detection methods there may flag this person as -being an outlier---being unusual on two variables, height and -weight---even though the pattern fits perfectly with our predictions. - -In the example below, we plot the raw data and see two possible -outliers. The first one falls along the regression line, and is -therefore ``in line'' with our hypothesis. The second one clearly -diverges from the regression line, and therefore we can conclude that -this outlier may have a disproportionate influence on our model. - -\begin{Shaded} -\begin{Highlighting}[] -\NormalTok{data }\OtherTok{\textless{}{-}}\NormalTok{ women[}\FunctionTok{rep}\NormalTok{(}\FunctionTok{seq\_len}\NormalTok{(}\FunctionTok{nrow}\NormalTok{(women)), }\AttributeTok{each =} \DecValTok{100}\NormalTok{), ]} -\NormalTok{data }\OtherTok{\textless{}{-}} \FunctionTok{rbind}\NormalTok{(data, }\FunctionTok{c}\NormalTok{(}\DecValTok{100}\NormalTok{, }\DecValTok{258}\NormalTok{), }\FunctionTok{c}\NormalTok{(}\DecValTok{100}\NormalTok{, }\DecValTok{200}\NormalTok{))} -\NormalTok{model }\OtherTok{\textless{}{-}} \FunctionTok{lm}\NormalTok{(weight }\SpecialCharTok{\textasciitilde{}}\NormalTok{ height, data)} -\NormalTok{rempsyc}\SpecialCharTok{::}\FunctionTok{nice\_scatter}\NormalTok{(data, }\StringTok{"height"}\NormalTok{, }\StringTok{"weight"}\NormalTok{)} -\end{Highlighting} -\end{Shaded} - -\begin{figure} -\includegraphics[width=1\linewidth]{paper_files/figure-latex/scatter-1} \caption{Scatter plot of height and weight, with two extreme observations: one model-consistent (top-right) and the other, model-inconsistent (i.e., an outlier; bottom-right).}\label{fig:scatter} -\end{figure} - -Using either the \emph{z}-score or MCD methods, our model-consistent -observation will be incorrectly flagged as an outlier or influential -observation. - -\begin{Shaded} -\begin{Highlighting}[] -\NormalTok{outliers }\OtherTok{\textless{}{-}} \FunctionTok{check\_outliers}\NormalTok{(model, }\AttributeTok{method =} \FunctionTok{c}\NormalTok{(}\StringTok{"zscore\_robust"}\NormalTok{, }\StringTok{"mcd"}\NormalTok{))} -\FunctionTok{which}\NormalTok{(outliers)} -\end{Highlighting} -\end{Shaded} - -\begin{verbatim} -#> [1] 1501 1502 -\end{verbatim} - -In contrast, the model-based detection method displays the desired -behaviour: it correctly flags the person who is very tall but very -light, without flagging the person who is both tall and heavy. - -\begin{Shaded} -\begin{Highlighting}[] -\NormalTok{outliers }\OtherTok{\textless{}{-}} \FunctionTok{check\_outliers}\NormalTok{(model, }\AttributeTok{method =} \StringTok{"cook"}\NormalTok{)} -\FunctionTok{which}\NormalTok{(outliers)} -\end{Highlighting} -\end{Shaded} - -\begin{verbatim} -#> [1] 1502 -\end{verbatim} - -\begin{Shaded} -\begin{Highlighting}[] -\FunctionTok{plot}\NormalTok{(outliers)} -\end{Highlighting} -\end{Shaded} - -\begin{figure} -\includegraphics[width=1\linewidth]{paper_files/figure-latex/model2-1} \caption{The leverage method (Cook's distance) correctly distinguishes the true outlier from the model-consistent extreme observation), based on the fitted model.}\label{fig:model2} -\end{figure} - -Finally, unusual observations happen naturally: extreme observations are -expected even when taken from a normal distribution. While statistical -models can integrate this ``expectation'', multivariate outlier methods -might be too conservative, flagging too many observations despite -belonging to the right generative process. For these reasons, we believe -that model-based methods are still preferable to the MCD when using -supported regression models. Additionally, if the presence of multiple -outliers is a significant concern, regression methods that are more -robust to outliers should be considered---like \emph{t} regression or -quantile regression---as they render their precise identification less -critical (McElreath, 2020). - -\hypertarget{composite-outlier-score}{% -\subsection{Composite Outlier Score}\label{composite-outlier-score}} - -The \emph{\{performance\}} package also offers an alternative, -consensus-based approach that combines several methods, based on the -assumption that different methods provide different angles of looking at -a given problem. By applying a variety of methods, one can hope to -``triangulate'' the true outliers (those consistently flagged by -multiple methods) and thus attempt to minimize false positives. - -In practice, this approach computes a composite outlier score, formed of -the average of the binary (0 or 1) classification results of each -method. It represents the probability that each observation is -classified as an outlier by at least one method. The default decision -rule classifies rows with composite outlier scores superior or equal to -0.5 as outlier observations (i.e., that were classified as outliers by -at least half of the methods). In \emph{\{performance\}}'s -\texttt{check\_outliers()}, one can use this approach by including all -desired methods in the corresponding argument. - -\begin{Shaded} -\begin{Highlighting}[] -\NormalTok{outliers }\OtherTok{\textless{}{-}} \FunctionTok{check\_outliers}\NormalTok{(model, }\AttributeTok{method =} \FunctionTok{c}\NormalTok{(}\StringTok{"zscore\_robust"}\NormalTok{, }\StringTok{"mcd"}\NormalTok{, }\StringTok{"cook"}\NormalTok{))} -\FunctionTok{which}\NormalTok{(outliers)} -\end{Highlighting} -\end{Shaded} - -\begin{verbatim} -#> [1] 1501 1502 -\end{verbatim} - -Outliers (counts or per variables) for individual methods can then be -obtained through attributes. For example: - -\begin{Shaded} -\begin{Highlighting}[] -\FunctionTok{attributes}\NormalTok{(outliers)}\SpecialCharTok{$}\NormalTok{outlier\_var}\SpecialCharTok{$}\NormalTok{zscore\_robust} -\end{Highlighting} -\end{Shaded} - -\begin{verbatim} -#> $weight -#> Row Distance_Zscore_robust -#> 1501 1501 6.913530 -#> 1502 1502 3.653492 -#> -#> $height -#> Row Distance_Zscore_robust -#> 1501 1501 5.901794 -#> 1502 1502 5.901794 -\end{verbatim} - -An example sentence for reporting the usage of the composite method -could be: - -\begin{quote} -Based on a composite outlier score (see the `check\_outliers()' function -in the `performance' R package, Lüdecke et al., 2021) obtained via the -joint application of multiple outliers detection algorithms ((a) median -absolute deviation (MAD)-based robust \emph{z} scores, Leys et al., -2013; (b) Mahalanobis minimum covariance determinant (MCD), Leys et al., -2019; and (c) Cook's distance, Cook, 1977), we excluded two participants -that were classified as outliers by at least half of the methods used. -\end{quote} - -\hypertarget{handling-outliers}{% -\section{Handling Outliers}\label{handling-outliers}} - -The above section demonstrated how to identify outliers using the -\texttt{check\_outliers()} function in the \emph{\{performance\}} -package. But what should we do with these outliers once identified? -Although it is common to automatically discard any observation that has -been marked as ``an outlier'' as if it might infect the rest of the data -with its statistical ailment, we believe that the use of SOD methods is -but one step in the get-to-know-your-data pipeline; a researcher or -analyst's \emph{domain knowledge} must be involved in the decision of -how to deal with observations marked as outliers by means of SOD. -Indeed, automatic tools can help detect outliers, but they are nowhere -near perfect. Although they can be useful to flag suspect data, they can -have misses and false alarms, and they cannot replace human eyes and -proper vigilance from the researcher. If you do end up manually -inspecting your data for outliers, it can be helpful to think of -outliers as belonging to different types of outliers, or categories, -which can help decide what to do with a given outlier. - -\hypertarget{error-interesting-and-random-outliers}{% -\subsection{Error, Interesting, and Random -Outliers}\label{error-interesting-and-random-outliers}} - -Leys et al. (2019) distinguish between error outliers, interesting -outliers, and random outliers. \emph{Error outliers} are likely due to -human error and should be corrected before data analysis or outright -removed since they are invalid observations. \emph{Interesting outliers} -are not due to technical error and may be of theoretical interest; it -might thus be relevant to investigate them further even though they -should be removed from the current analysis of interest. \emph{Random -outliers} are assumed to be due to chance alone and to belong to the -correct distribution and, therefore, should be retained. - -It is recommended to \emph{keep} observations which are expected to be -part of the distribution of interest, even if they are outliers (Leys et -al., 2019). However, if it is suspected that the outliers belong to an -alternative distribution, then those observations could have a large -impact on the results and call into question their robustness, -especially if significance is conditional on their inclusion, so should -be removed. - -On the other hand, there are also outliers that cannot be detected by -statistical tools, but should be found and removed. For example, if we -are studying the effects of X on Y among teenagers and we have one -observation from a 20-year-old, this observation might not be a -\emph{statistical outlier}, but it is an outlier in the \emph{context} -of our research, and should be discarded to allow for valid inferences. - -\hypertarget{winsorization}{% -\subsection{Winsorization}\label{winsorization}} - -\emph{Removing} outliers can in this case be a valid strategy, and -ideally one would report results with and without outliers to see the -extent of their impact on results. This approach however can reduce -statistical power. Therefore, some propose a \emph{recoding} approach, -namely, winsorization: bringing outliers back within acceptable limits -(e.g., 3 MADs, Tukey \& McLaughlin, 1963). However, if possible, it is -recommended to collect enough data so that even after removing outliers, -there is still sufficient statistical power without having to resort to -winsorization (Leys et al., 2019). - -The \emph{easystats} ecosystem makes it easy to incorporate this step -into your workflow through the \texttt{winsorize()} function of -\emph{\{datawizard\}}, a lightweight R package to facilitate data -wrangling and statistical transformations (Patil et al., 2022). This -procedure will bring back univariate outliers within the limits of -`acceptable' values, based either on the percentile, the \emph{z} score, -or its robust alternative based on the MAD. - -\begin{Shaded} -\begin{Highlighting}[] -\NormalTok{data[}\DecValTok{1501}\SpecialCharTok{:}\DecValTok{1502}\NormalTok{, ] }\CommentTok{\# See outliers rows} -\end{Highlighting} -\end{Shaded} - -\begin{verbatim} -#> height weight -#> 1501 100 258 -#> 1502 100 200 -\end{verbatim} - -\begin{Shaded} -\begin{Highlighting}[] -\CommentTok{\# Winsorizing using the MAD} -\FunctionTok{library}\NormalTok{(datawizard)} -\NormalTok{winsorized\_data }\OtherTok{\textless{}{-}} \FunctionTok{winsorize}\NormalTok{(data, }\AttributeTok{method =} \StringTok{"zscore"}\NormalTok{, }\AttributeTok{robust =} \ConstantTok{TRUE}\NormalTok{, }\AttributeTok{threshold =} \DecValTok{3}\NormalTok{)} - -\CommentTok{\# Values \textgreater{} +/{-} MAD have been winsorized} -\NormalTok{winsorized\_data[}\DecValTok{1501}\SpecialCharTok{:}\DecValTok{1502}\NormalTok{, ]} -\end{Highlighting} -\end{Shaded} - -\begin{verbatim} -#> height weight -#> 1501 82.7912 188.3736 -#> 1502 82.7912 188.3736 -\end{verbatim} - -\hypertarget{the-importance-of-transparency}{% -\subsection{The Importance of -Transparency}\label{the-importance-of-transparency}} - -Once again, it is a critical part of a sound outlier treatment that -regardless of which SOD method used, it should be reported in a -reproducible manner. Ideally, the handling of outliers should be -specified \emph{a priori} with as much detail as possible, and -preregistered, to limit researchers' degrees of freedom and therefore -risks of false positives (Leys et al., 2019). This is especially true -given that interesting outliers and random outliers are often times hard -to distinguish in practice. Thus, researchers should always prioritize -transparency and report all of the following information: (a) how many -outliers were identified (including percentage); (b) according to which -method and criteria, (c) using which function of which R package (if -applicable), and (d) how they were handled (excluded or winsorized, if -the latter, using what threshold). If at all possible, (e) the -corresponding code script along with the data should be shared on a -public repository like the Open Science Framework (OSF), so that the -exclusion criteria can be reproduced precisely. - -\hypertarget{conclusion}{% -\section{Conclusion}\label{conclusion}} - -In this paper, we have showed how to investigate outliers using the -\texttt{check\_outliers()} function of the \emph{\{performance\}} -package while following current good practices. However, best practice -for outlier treatment does not stop at using appropriate statistical -algorithms, but entails respecting existing recommendations, such as -preregistration, reproducibility, consistency, transparency, and -justification. Ideally, one would additionally also report the package, -function, and threshold used (linking to the full code when possible). -We hope that this paper and the accompanying \texttt{check\_outlier()} -function of \emph{easystats} will help researchers engage in good -research practices while providing a smooth outlier detection -experience. - -\hypertarget{contributions}{% -\subsubsection{Contributions}\label{contributions}} - -Author 1 drafted the paper; all authors contributed to both the writing -of the paper and the conception of the software. - -\hypertarget{acknowledgements}{% -\subsubsection{Acknowledgements}\label{acknowledgements}} - -\emph{\{performance\}} is part of the collaborative -\href{https://github.com/easystats/easystats}{\emph{easystats}} -ecosystem (Lüdecke et al., 2019/2023). Thus, we thank all -\href{https://github.com/orgs/easystats/people}{members of easystats}, -contributors, and users alike. - -\hypertarget{funding-information}{% -\subsubsection{Funding information}\label{funding-information}} - -This research received no external funding. - -\hypertarget{competing-interests}{% -\subsubsection{Competing Interests}\label{competing-interests}} - -The authors declare no conflict of interest - -\hypertarget{references}{% -\section*{References}\label{references}} -\addcontentsline{toc}{section}{References} - -\hypertarget{refs}{} -\begin{CSLReferences}{1}{0} -\leavevmode\vadjust pre{\hypertarget{ref-cook1977detection}{}}% -Cook, R. D. (1977). Detection of influential observation in linear -regression. \emph{Technometrics}, \emph{19}(1), 15--18. -\url{https://doi.org/10.1080/00401706.1977.10489493} - -\leavevmode\vadjust pre{\hypertarget{ref-gnanadesikan1972robust}{}}% -Gnanadesikan, R., \& Kettenring, J. R. (1972). Robust estimates, -residuals, and outlier detection with multiresponse data. -\emph{Biometrics}, 81--124. - -\leavevmode\vadjust pre{\hypertarget{ref-leys2019outliers}{}}% -Leys, C., Delacre, M., Mora, Y. L., Lakens, D., \& Ley, C. (2019). How -to classify, detect, and manage univariate and multivariate outliers, -with emphasis on pre-registration. \emph{International Review of Social -Psychology}. \url{https://doi.org/10.5334/irsp.289} - -\leavevmode\vadjust pre{\hypertarget{ref-leys2018outliers}{}}% -Leys, C., Klein, O., Dominicy, Y., \& Ley, C. (2018). Detecting -multivariate outliers: Use a robust variant of the mahalanobis distance. -\emph{Journal of Experimental Social Psychology}, \emph{74}, 150--156. -\url{https://doi.org/10.1016/j.jesp.2017.09.011} - -\leavevmode\vadjust pre{\hypertarget{ref-leys2013outliers}{}}% -Leys, C., Ley, C., Klein, O., Bernard, P., \& Licata, L. (2013). -Detecting outliers: Do not use standard deviation around the mean, use -absolute deviation around the median. \emph{Journal of Experimental -Social Psychology}, \emph{49}(4), 764--766. -\url{https://doi.org/10.1016/j.jesp.2013.03.013} - -\leavevmode\vadjust pre{\hypertarget{ref-ludecke2021performance}{}}% -Lüdecke, D., Ben-Shachar, M. S., Patil, I., Waggoner, P., \& Makowski, -D. (2021). {performance}: An r package for assessment, comparison and -testing of statistical models. \emph{Journal of Open Source Software}, -\emph{6}(60), 3139. \url{https://doi.org/10.21105/joss.03139} - -\leavevmode\vadjust pre{\hypertarget{ref-easystatspackage}{}}% -Lüdecke, D., Makowski, D., Ben-Shachar, M. S., Patil, I., Wiernik, B. -M., Bacher, E., \& Thériault, R. (2023). \emph{{easystats}: Streamline -model interpretation, visualization, and reporting}. -\url{https://easystats.github.io/easystats/} (Original work published -2019) - -\leavevmode\vadjust pre{\hypertarget{ref-mcelreath2020statistical}{}}% -McElreath, R. (2020). \emph{Statistical rethinking: A bayesian course -with examples in {R} and stan}. CRC press. - -\leavevmode\vadjust pre{\hypertarget{ref-patil2022datawizard}{}}% -Patil, I., Makowski, D., Ben-Shachar, M. S., Wiernik, B. M., Bacher, E., -\& Lüdecke, D. (2022). {datawizard}: An {R} package for easy data -preparation and statistical transformations. \emph{Journal of Open -Source Software}, \emph{7}(78), 4684. -\url{https://doi.org/10.21105/joss.04684} - -\leavevmode\vadjust pre{\hypertarget{ref-ratcliff1993methods}{}}% -Ratcliff, R. (1993). 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Statistical mimicking of reaction -time data: Single-process models, parameter variability, and mixtures. -\emph{Psychonomic Bulletin \& Review}, \emph{2}(1), 20--54. -\url{https://doi.org/10.3758/BF03214411} - -\end{CSLReferences} - -\bibliographystyle{unsrt} -\bibliography{mybibfile.bib} - - -\end{document} diff --git a/papers/Collabra/paper_files/Editor comments.pdf b/papers/Collabra/paper_files/Editor comments.pdf deleted file mode 100644 index e479999f9b2510caa767a6a95e18849e43f14c1e..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 190532 zcmb@u2Q=K@*Efpj1fxd@MlhncM6WXliC!XFM33IPQDbzX_f8TmND!UqT@ock?=3om zG2XA=|Nq?QzW2TBz0dosYt34$`JQw3+2!oB_h;`fHVvpEj{vVQA=}U0?PWp%W`1U; zH*X0gCHWLwEzR7WT$v#+oP2HV?alZ^c=?%)Ao{kB7EWGn%xXH!0{p!E63oCCPlP3y zy`KmhaWcy}JKJ08TfR}Xb>|Zidde&G1el_#tn=bIH?zI1oh7r9rMaCGFi^q9)yct< zPe4GB7gz;YS=-FY%+>balQ;?aG+do5Jj^Wt`r3B3W_-XlnH_-9z>|MAX6xh#HFLLQ zhCsyy`2~geg$14phzW`cigEGta{wP;+zTg*|NRhYX+leY8Gv1(|76?Tj9Gw?PyPin 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