diff --git a/docs/articles/IBD.html b/docs/articles/IBD.html index d96b562..6cf79fd 100644 --- a/docs/articles/IBD.html +++ b/docs/articles/IBD.html @@ -132,13 +132,12 @@

Microbiome - Metabolome Mediation Analysis

Data Processing

-

We’ll load data from the Borenstein Lab’s microbiome-metabolome -curated data repository. This is a great resource that consistently -documents each study and ensures uniform data processing. Our data is -from Franzosa et -al.’s study of intestinal bowel disease. We’ll treat disease status -as the treatment, the microbiome as mediators, and metabolites as the -outcome, in the spirit of that study’s discussion:

+

We’ll load data from the Borenstein Lab’s microbiome-metabolome curated data +repository. This is a great resource that consistently documents each +study and ensures uniform data processing. Our data is from Franzosa et al.’s study of +intestinal bowel disease. We’ll treat disease status as the treatment, +the microbiome as mediators, and metabolites as the outcome, in the +spirit of that study’s discussion:

Together, these findings suggest that yet-to-be characterized molecules in the gut metabolome, linked to inflammation and ultimately @@ -146,9 +145,9 @@

Data Processing 
 Sys.setenv("VROOM_CONNECTION_SIZE" = 5e6)
-taxa <- read_tsv("https://raw.githubusercontent.com/borenstein-lab/microbiome-metabolome-curated-data/main/data/processed_data/FRANZOSA_IBD_2019/genera.tsv")[, -1]
-metabolites <- read_tsv("https://raw.githubusercontent.com/borenstein-lab/microbiome-metabolome-curated-data/main/data/processed_data/FRANZOSA_IBD_2019/mtb.tsv")[, -1]
-metadata <- read_tsv("https://github.com/borenstein-lab/microbiome-metabolome-curated-data/raw/main/data/processed_data/FRANZOSA_IBD_2019/metadata.tsv")
+taxa <- read_tsv("https://go.wisc.edu/l015v0")[, -1] +metabolites <- read_tsv("https://go.wisc.edu/0t3gs3")[, -1] +metadata <- read_tsv("https://go.wisc.edu/9z36wr")

We’ll filter quite aggressively so that the examples in this vignette run quickly. We then compile everything into a mediation_data object that organizes the treatment, @@ -159,23 +158,23 @@

Data Processing.Rmd source.

 taxa <- clr(taxa) |>
-  filter_mean() |>
-  simplify_tax_names()
+    filter_mean() |>
+    simplify_tax_names()
 
 metabolites <- log(1 + metabolites) |>
-  filter_mean(threshold = 6) |>
-  select(matches(annotated_metabolites(metabolites))) |>
-  simplify_metab_names()
+    filter_mean(threshold = 6) |>
+    select(matches(annotated_metabolites(metabolites))) |>
+    simplify_metab_names()
 
 combined <- metabolites |>
-  bind_cols(taxa, metadata) |>
-  as_tibble()
+    bind_cols(taxa, metadata) |>
+    as_tibble()
 
 exper <- mediation_data(
-  combined,
-  colnames(metabolites),
-  "Study.Group",
-  colnames(taxa)
+    combined,
+    colnames(metabolites),
+    "Study.Group",
+    colnames(taxa)
 )
 
 exper
@@ -193,7 +192,7 @@

Lasso Approach 
 model <- multimedia(exper, glmnet_model(lambda = 0.1)) |>
-  estimate(exper)
+ estimate(exper)

We can have different direct effects depending on the treatment assignments of the mediators. Here we’ll average over all mediator settings and plot the features with the largest direct effects. Note @@ -202,25 +201,29 @@

Lasso Approach 
 direct <- list(
-  CD = direct_effect(model, exper, 1, 3),
-  UC = direct_effect(model, exper, 2, 3)
+    CD = direct_effect(model, exper, 1, 3),
+    UC = direct_effect(model, exper, 2, 3)
 ) |>
-  map_dfr(effect_summary, .id = "treatment")
+    map_dfr(effect_summary, .id = "treatment")
 
 vis_direct <- direct |>
-  slice_max(abs(direct_effect), n = 20) |>
-  pull(outcome)
+    slice_max(abs(direct_effect), n = 20) |>
+    pull(outcome)
 
 combined |>
-  select(any_of(vis_direct), Study.Group) |>
-  pivot_longer(-Study.Group, names_to = "feature") |>
-  ggplot() +
-  geom_boxplot(aes(value, reorder(feature, value, median), fill = Study.Group)) +
-  labs(
-    x = "log(1 + intensity)",
-    y = "Metabolite",
-    fill = "Group"
-  )
+ select(any_of(vis_direct), Study.Group) |> + pivot_longer(-Study.Group, names_to = "feature") |> + ggplot() + + geom_boxplot( + aes(value, reorder(feature, value, median), + fill = Study.Group + ) + ) + + labs( + x = "log(1 + intensity)", + y = "Metabolite", + fill = "Group" + )

The block below calculates the analogous overall indirect effects. We’re particularly interested in the difference between metabolites that @@ -230,19 +233,25 @@

Lasso Approachtop_effects.

 indirect_effect <- list(
-  CD = indirect_overall(model, exper, 1, 3),
-  UC = indirect_overall(model, exper, 2, 3)
+    CD = indirect_overall(model, exper, 1, 3),
+    UC = indirect_overall(model, exper, 2, 3)
 )
 
 top_direct <- dplyr::rename(direct, effect = direct_effect)
-top_indirect <- dplyr::rename(bind_rows(indirect_effect), effect = indirect_effect)
+top_indirect <- dplyr::rename(bind_rows(indirect_effect),
+    effect = indirect_effect
+)
 top_effects <- list(direct = top_direct, indirect = top_indirect) |>
-  bind_rows(.id = "type")
+    bind_rows(.id = "type")
 
-vis_outcomes <- c("m0181_hydrocinnamic_acid", "m1303_lithocholate", "m0036_creatinine", "m0253_sphingosine", "m1478_C182_CE", "m0295_arginine")
+vis_outcomes <- c(
+    "m0181_hydrocinnamic_acid", "m1303_lithocholate",
+    "m0036_creatinine", "m0253_sphingosine", "m1478_C182_CE",
+    "m0295_arginine"
+)
 top_effects <- bind_rows(
-  filter(top_effects, outcome %in% vis_outcomes[1:3], type == "indirect"),
-  filter(top_effects, outcome %in% vis_outcomes[4:6], type == "direct"),
+    filter(top_effects, outcome %in% vis_outcomes[1:3], type == "indirect"),
+    filter(top_effects, outcome %in% vis_outcomes[4:6], type == "direct"),
 )

The plot below is an MDS of microbiome compositions where point sizes represent metabolite abundances. Notice that the for indirect effects, @@ -255,23 +264,26 @@

Lasso Approach mds <- cmdscale(dist(mediators(exper)), eig = TRUE, k = 2) coords <- data.frame(mds$points) |> - bind_cols(treatments(exper)) |> - bind_cols(outcomes(exper)[, vis_outcomes]) |> - pivot_longer(top_effects$outcome, names_to = "outcome", values_to = "abundance") |> - left_join(top_effects) |> - group_by(outcome) |> - mutate(abundance_quantile = as.integer(as.factor(cut(abundance, 10))) / 10) + bind_cols(treatments(exper)) |> + bind_cols(outcomes(exper)[, vis_outcomes]) |> + pivot_longer(top_effects$outcome, + names_to = "outcome", + values_to = "abundance" + ) |> + left_join(top_effects) |> + group_by(outcome) |> + mutate(abundance_quantile = as.integer(as.factor(cut(abundance, 10))) / 10) ggplot(coords) + - geom_point(aes(X1, X2, col = Study.Group, size = abundance_quantile)) + - scale_size_area(max_size = 1.5, breaks = c(0.25, 0.5, 0.75)) + - labs( - x = glue("MDS1 [{eig(mds$eig, 1)}%]"), - y = glue("MDS2 [{eig(mds$eig, 2)}%]"), - size = "Metabolite Abundance Quantile", - col = "Group" - ) + - facet_wrap(~ type + reorder(outcome, -abundance)) + geom_point(aes(X1, X2, col = Study.Group, size = abundance_quantile)) + + scale_size_area(max_size = 1.5, breaks = c(0.25, 0.5, 0.75)) + + labs( + x = glue("MDS1 [{eig(mds$eig, 1)}%]"), + y = glue("MDS2 [{eig(mds$eig, 2)}%]"), + size = "Metabolite Abundance Quantile", + col = "Group" + ) + + facet_wrap(~ type + reorder(outcome, -abundance))

Pathwise indirect effects are those that appear when modifying the treatment status for a single mediator. Unlike overall indirect effects, @@ -287,7 +299,7 @@

Lasso Approach# ) |> # map_dfr(effect_summary, .id = "treatment") -indirect_sorted <- read_csv("https://drive.google.com/uc?export=download&id=1Ar7u2rU7DLMjvS-iV9OXwGcY4Rs1Q5wI") +indirect_sorted <- read_csv("https://go.wisc.edu/n04p94")

We can look at the effects which have the strongest indirect effects. These make sense. For example, genus Biophila seems to have a negative relationship with Taurine. Maybe that metabolite is produced by a @@ -296,9 +308,9 @@

Lasso Approach 
 p <- indirect_sorted %>%
-  split(.$treatment) |>
-  map(~ arrange(., -indirect_effect) |>
-    plot_mediators(exper, treatment = "Study.Group", nrow = 2))
+    split(.$treatment) |>
+    map(~ arrange(., -indirect_effect) |>
+        plot_mediators(exper, treatment = "Study.Group", nrow = 2))
 
 p[["CD"]]

@@ -310,25 +322,25 @@

Lasso Approach 
 altered <- model |>
-  nullify("T->Y") |>
-  estimate(exper)
+    nullify("T->Y") |>
+    estimate(exper)
 
 # sample at original treatment assignments
 profile <- setup_profile(model, treatments(exper), treatments(exper))
 samples <- list(
-  real = outcomes(exper),
-  fitted = outcomes(sample(model, profile = profile)),
-  altered = outcomes(sample(altered, profile = profile))
+    real = outcomes(exper),
+    fitted = outcomes(sample(model, profile = profile)),
+    altered = outcomes(sample(altered, profile = profile))
 ) |>
-  bind_rows(.id = "source") |>
-  bind_cols(treatment = rep(treatments(exper)$Study.Group, 3)) |>
-  pivot_longer(direct$outcome) |>
-  mutate(name = factor(name, levels = unique(direct$outcome)))
+    bind_rows(.id = "source") |>
+    bind_cols(treatment = rep(treatments(exper)$Study.Group, 3)) |>
+    pivot_longer(direct$outcome) |>
+    mutate(name = factor(name, levels = unique(direct$outcome)))
 
 # visualize
 ggplot(filter(samples, samples$name %in% unique(samples$name)[1:20])) +
-  geom_boxplot(aes(value, name, fill = treatment)) +
-  facet_wrap(~source)
+ geom_boxplot(aes(value, name, fill = treatment)) + + facet_wrap(~source)

How can we understand the uncertainty of the estimated models? One approach is to form the bootstrap distribution of the effects that we @@ -339,38 +351,38 @@

Lasso Approach 
 fs <- list(direct = direct_effect, indirect = indirect_overall)
-#inference <- bootstrap(model, exper, fs, B = 1000)
-inference <- readRDS(url("https://drive.google.com/uc?export=download&id=16A9MCblgf327SiL0hataAHYfs38wB_K1"))
+# inference <- bootstrap(model, exper, fs, B = 1000) +inference <- readRDS(url("https://go.wisc.edu/33ty1f")) 
 filter_outcomes <- inference$indirect |>
-  effect_summary() |>
-  group_by(outcome) |>
-  summarise(indirect_effect = median(indirect_effect)) |>
-  slice_max(abs(indirect_effect), n = 20) |>
-  pull(outcome)
+    effect_summary() |>
+    group_by(outcome) |>
+    summarise(indirect_effect = median(indirect_effect)) |>
+    slice_max(abs(indirect_effect), n = 20) |>
+    pull(outcome)
 
 p1 <- filter(inference$indirect, outcome %in% filter_outcomes) |>
-  ggplot() +
-  geom_vline(xintercept = 0) +
-  stat_slabinterval(
-    aes(indirect_effect, reorder(outcome, indirect_effect, median)),
-    .width = c(.66, .95)
-  ) +
-  labs(x = "Indirect Effect", y = "Metabolite")
+    ggplot() +
+    geom_vline(xintercept = 0) +
+    stat_slabinterval(
+        aes(indirect_effect, reorder(outcome, indirect_effect, median)),
+        .width = c(.66, .95)
+    ) +
+    labs(x = "Indirect Effect", y = "Metabolite")
 
 filter_outcomes <- inference$direct |>
-  group_by(outcome) |>
-  summarise(direct_effect = median(direct_effect)) |>
-  slice_max(abs(direct_effect), n = 20) |>
-  pull(outcome)
+    group_by(outcome) |>
+    summarise(direct_effect = median(direct_effect)) |>
+    slice_max(abs(direct_effect), n = 20) |>
+    pull(outcome)
 p2 <- filter(inference$direct, outcome %in% filter_outcomes) |>
-  ggplot() +
-  geom_vline(xintercept = 0) +
-  stat_slabinterval(
-    aes(direct_effect, reorder(outcome, direct_effect, median)),
-    .width = c(.66, .95)
-  ) +
-  labs(x = "Direct Effect", y = "Metabolite")
+    ggplot() +
+    geom_vline(xintercept = 0) +
+    stat_slabinterval(
+        aes(direct_effect, reorder(outcome, direct_effect, median)),
+        .width = c(.66, .95)
+    ) +
+    labs(x = "Direct Effect", y = "Metabolite")
 
 p1 | p2

@@ -401,7 +413,7 @@

Hurdle-Lognormal Approach# brms_model(family = hurdle_lognormal()) # ) |> # estimate(exper2) -model <- readRDS(url("https://uwmadison.box.com/shared/static/803fpu7skhjpd8f5ye6pb3crkc67qhl1.rds")) +model <- readRDS(url("https://go.wisc.edu/5e26op"))

With the updated model, we can again compute pathwise indirect effects. This time, we are more sensitive to metabolites that completely vanish in the IBD (treatment) group. In all of the selected pairs, there @@ -409,9 +421,9 @@

Hurdle-Lognormal Approach 
-#indirect_sorted <- indirect_pathwise(model, exper2) |>
-indirect_sorted <- read_csv("https://drive.google.com/uc?export=download&id=1aX6h98udBxqR3RBOjbUnoY1wLMfFUceB") |>
-  effect_summary()
+# indirect_sorted <- indirect_pathwise(model, exper2) |>
+indirect_sorted <- read_csv("https://go.wisc.edu/j3z503") |>
+    effect_summary()
 plot_mediators(indirect_sorted, exper2, treatment = "Study.Group")

We can see how well the hurdle model captured the zero pattern by @@ -436,16 +448,16 @@

Hurdle-Lognormal Approach 
-#direct <- direct_effect(model, exper) |>
-direct <- read_csv("https://drive.google.com/uc?export=download&id=10dYU4ahizRk7hjsi6JKJWdNKdAI1qyXS") |>
-  effect_summary()
+# direct <- direct_effect(model, exper) |>
+direct <- read_csv("https://go.wisc.edu/3ik252") |>
+    effect_summary()
 
 combined |>
-  select(any_of(direct$outcome), Study.Group) |>
-  pivot_longer(-Study.Group, names_to = "feature") |>
-  mutate(feature = factor(feature, levels = unique(direct$outcome))) |>
-  ggplot() +
-  geom_boxplot(aes(value, feature, fill = Study.Group))
+ select(any_of(direct$outcome), Study.Group) |> + pivot_longer(-Study.Group, names_to = "feature") |> + mutate(feature = factor(feature, levels = unique(direct$outcome))) |> + ggplot() + + geom_boxplot(aes(value, feature, fill = Study.Group))

@@ -499,7 +511,7 @@

Hurdle-Lognormal Approach#> [34] iterators_1.0.14 pkgconfig_2.0.3 Matrix_1.7-0 #> [37] R6_2.5.1 fastmap_1.2.0 glmnetUtils_1.1.9 #> [40] GenomeInfoDbData_1.2.12 digest_0.6.37 colorspace_2.1-1 -#> [43] textshaping_0.4.0 vegan_2.6-6.1 labeling_0.4.3 +#> [43] textshaping_0.4.0 vegan_2.6-8 labeling_0.4.3 #> [46] timechange_0.3.0 fansi_1.0.6 httr_1.4.7 #> [49] abind_1.4-5 mgcv_1.9-1 compiler_4.4.1 #> [52] bit64_4.0.5 withr_3.0.1 backports_1.5.0 diff --git a/docs/articles/illustration.html b/docs/articles/illustration.html index b1d720e..51950e5 100644 --- a/docs/articles/illustration.html +++ b/docs/articles/illustration.html @@ -117,19 +117,19 @@

Illustration with Nonlinear Effects

#' Helper to plot the real data plot_exper <- function(fit, profile) { - pivot_samples(fit, profile) |> - ggplot() + - geom_point(aes(mediator, value, col = factor(treatment))) + - facet_grid(. ~ outcome) + - theme(legend.position = "bottom") + pivot_samples(fit, profile) |> + ggplot() + + geom_point(aes(mediator, value, col = factor(treatment))) + + facet_grid(. ~ outcome) + + theme(legend.position = "bottom") } #' Convert a SummarizedExperiment to long form pivot_samples <- function(fit, profile) { - exper_sample <- sample(fit, profile = profile) - outcomes(exper_sample) |> - bind_cols(mediators(exper_sample), t_outcome) |> - pivot_longer(starts_with("outcome"), names_to = "outcome") + exper_sample <- sample(fit, profile = profile) + outcomes(exper_sample) |> + bind_cols(mediators(exper_sample), t_outcome) |> + pivot_longer(starts_with("outcome"), names_to = "outcome") }

We will consdier a mediation analysis with two outcomes and a single mediator. The toy dataset below is included in the package – you can @@ -139,22 +139,27 @@

Illustration with Nonlinear Effects

for the direct effect.

 xy_data <- demo_spline()
-xy_long <- list(true = pivot_longer(xy_data, starts_with("outcome"), names_to = "outcome"))
+xy_long <- list( + true = pivot_longer(xy_data, starts_with("outcome"), names_to = "outcome") +)

The block below estimates a random forest model on these randomly generated data (after first converting them into an object of class mediation_data). We can vary ranger parameters using the arguments to rf_model().

-exper <- mediation_data(xy_data, starts_with("outcome"), "treatment", "mediator")
+exper <- mediation_data(
+    xy_data, starts_with("outcome"), "treatment", "mediator"
+)
+
 fit <- multimedia(
-  exper,
-  outcome_estimator = rf_model(num.trees = 1e3)
+    exper,
+    outcome_estimator = rf_model(num.trees = 1e3)
 ) |>
-  estimate(exper)
+ estimate(exper)

Let’s look at the estimated effects.

 direct_effect(fit) |>
-  effect_summary()
+ effect_summary() 
#> # A tibble: 2 × 2
 #>   outcome   direct_effect
 #>                
@@ -163,7 +168,7 @@ 
Illustration with Nonlinear Effects

 
+    effect_summary()
#> # A tibble: 2 × 2
 #>   outcome   indirect_effect
 #>                  
@@ -176,19 +181,21 @@ 
Illustration with Nonlinear Effects

 estimate?

 
 confound_ix <- expand.grid(mediator = 1, outcome = 1:2)
-#sensitivity_curve <- sensitivity(fit, exper, confound_ix)
-sensitivity_curve <- read_csv("https://drive.google.com/uc?export=download&id=1fEhg-aMRyfhAjgcJmsrxz2cmWCOdnM6C")
+# sensitivity_curve <- sensitivity(fit, exper, confound_ix)
+sensitivity_curve <- read_csv("https://go.wisc.edu/0xcyr1")
 plot_sensitivity(sensitivity_curve)

 

 
 perturb <- matrix(
-  c(0, 3, 0,
-    3, 0, 0,
-    0, 0, 0),
-  nrow = 3, byrow = TRUE
+    c(
+        0, 3, 0,
+        3, 0, 0,
+        0, 0, 0
+    ),
+    nrow = 3, byrow = TRUE
 )
-#sensitivity_curve <- sensitivity_perturb(fit, exper, perturb)
-sensitivity_curve <- read_csv("https://drive.google.com/uc?export=download&id=1CkCdaAbiVeoo7ILYB1PavFzqiFb1N08A")
+# sensitivity_curve <- sensitivity_perturb(fit, exper, perturb)
+sensitivity_curve <- read_csv("https://go.wisc.edu/75mz1b")
 plot_sensitivity(sensitivity_curve, x_var = "nu")

 

 
If we want to look at samples at new treatment assignments, we have
@@ -204,75 +211,79 @@ 
Illustration with Nonlinear Effects

 assumes a linear, rather than random forest, outcome model.

 
 altered_m <- nullify(fit, "T->M") |>
-  estimate(exper)
+    estimate(exper)
 altered_ty <- nullify(fit, "T->Y") |>
-  estimate(exper)
+    estimate(exper)
 
 fit_lm <- multimedia(
-  exper,
-  outcome_estimator = lm_model()
+    exper,
+    outcome_estimator = lm_model()
 ) |>
-  estimate(exper)

+    estimate(exper)

We can sample from these models and organize the results into one long data.frame. The function pivot_samples is defined at the top of the script.

-xy_long <- c(
-  xy_long,
-  list(
-    altered_m = pivot_samples(altered_m, profile),
-    altered_ty = pivot_samples(altered_ty, profile),
-    linear = pivot_samples(fit_lm, profile)
-  )
-) |>
-  bind_rows(.id = "fit_type") |>
-  mutate(
-    fit_type = case_when(
-      fit_type == "linear" ~ "Linear Model",
-      fit_type == "true" ~ "Original Data",
-      fit_type == "fitted" ~ "RF (Full)",
-      fit_type == "altered_ty" ~ "RF (T-\\->Y)",
-      fit_type == "altered_m" ~ "RF (T-\\->M)"
-    ),
-    fit_type = factor(fit_type, levels = c("Original Data", "RF (Full)", "RF (T-\\->M)", "RF (T-\\->Y)", "Linear Model")),
-    outcome = case_when(
-      outcome == "outcome_1" ~ "Y[1]",
-      outcome == "outcome_2" ~ "Y[2]"
+pretty_labels <- c(
+    "Original Data", "RF (Full)", "RF (T-\\->M)", "RF (T-\\->Y)", "Linear Model"
+)
+
+xy_long <- c(
+    xy_long,
+    list(
+        altered_m = pivot_samples(altered_m, profile),
+        altered_ty = pivot_samples(altered_ty, profile),
+        linear = pivot_samples(fit_lm, profile)
     )
-  )
+) |> + bind_rows(.id = "fit_type") |> + mutate( + fit_type = case_when( + fit_type == "linear" ~ "Linear Model", + fit_type == "true" ~ "Original Data", + fit_type == "fitted" ~ "RF (Full)", + fit_type == "altered_ty" ~ "RF (T-\\->Y)", + fit_type == "altered_m" ~ "RF (T-\\->M)" + ), + fit_type = factor(fit_type, levels = pretty_labels), + outcome = case_when( + outcome == "outcome_1" ~ "Y[1]", + outcome == "outcome_2" ~ "Y[2]" + ) + )

The figure below compares the original data and model with the various nullified versions, using the combined xy_long dataset constructed above.

 xy_long |>
-  sample_frac(size = 0.1) |>
-  ggplot(aes(mediator, col = treatment)) +
-  geom_point(aes(y = value), size = 0.4, alpha = 0.9) +
-  geom_rug(alpha = 0.99, linewidth = 0.1) +
-  facet_grid(outcome ~ fit_type) +
-  labs(x = expression("Mediator M"), y = "Outcome", col = "Treatment") +
-  theme(
-    strip.text = element_text(size = 11),
-    axis.title = element_text(size = 14),
-    legend.title = element_text(size = 12)
-  )
+ sample_frac(size = 0.1) |> + ggplot(aes(mediator, col = treatment)) + + geom_point(aes(y = value), size = 0.4, alpha = 0.9) + + geom_rug(alpha = 0.99, linewidth = 0.1) + + facet_grid(outcome ~ fit_type) + + labs(x = expression("Mediator M"), y = "Outcome", col = "Treatment") + + theme( + strip.text = element_text(size = 11), + axis.title = element_text(size = 14), + legend.title = element_text(size = 12) + )

We can calculate bootstrap confidence intervals for the direct and overall indirect effects using the block below.

 fs <- list(direct_effect = direct_effect, indirect_overall = indirect_overall)
-#bootstraps <- bootstrap(fit, exper, fs = fs)
-bootstraps <- readRDS(url("https://drive.google.com/uc?export=download&id=1vhWcY5UruCyLNJbTDTVFLBHV_6ITQdYT"))
+# bootstraps <- bootstrap(fit, exper, fs = fs)
+bootstraps <- readRDS(url("https://go.wisc.edu/977l04"))
 
 ggplot(bootstraps$direct_effect) +
-  geom_histogram(aes(direct_effect)) +
-  facet_wrap(~outcome)
+ geom_histogram(aes(direct_effect)) + + facet_wrap(~outcome) 

 
 ggplot(bootstraps$indirect_overall) +
-  geom_histogram(aes(indirect_effect)) +
-  facet_wrap(~outcome)
+ geom_histogram(aes(indirect_effect)) + + facet_wrap(~outcome) 

 sessionInfo()
@@ -325,7 +336,7 @@

Illustration with Nonlinear Effects

#> [40] bookdown_0.40 iterators_1.0.14 knitr_1.48 #> [43] timechange_0.3.0 Matrix_1.7-0 splines_4.4.1 #> [46] igraph_2.0.3 abind_1.4-5 yaml_2.3.10 -#> [49] vegan_2.6-6.1 codetools_0.2-20 curl_5.2.1 +#> [49] vegan_2.6-8 codetools_0.2-20 curl_5.2.1 #> [52] lattice_0.22-6 plyr_1.8.9 withr_3.0.1 #> [55] evaluate_0.24.0 desc_1.4.3 survival_3.7-0 #> [58] Biostrings_2.73.1 pillar_1.9.0 BiocManager_1.30.24 diff --git a/docs/articles/mindfulness.html b/docs/articles/mindfulness.html index 4fc383c..b557eb5 100644 --- a/docs/articles/mindfulness.html +++ b/docs/articles/mindfulness.html @@ -132,11 +132,11 @@

The Mindfulness Study

different baseline behavioral and microbiome profiles.

 exper <- mediation_data(
-  mindfulness,
-  taxa_names(mindfulness),
-  "treatment",
-  starts_with("mediator"),
-  "subject"
+    mindfulness,
+    taxa_names(mindfulness),
+    "treatment",
+    starts_with("mediator"),
+    "subject"
 )
 
 exper
@@ -155,21 +155,21 @@

The Mindfulness Study

 # use Flavonifractor as the reference for the log-ratio transform
 outcomes(exper) <- outcomes(exper) |>
-  select(Flavonifractor, everything())
+    select(Flavonifractor, everything())
 
 model <- multimedia(
-  exper,
-  lnm_model(seed = .Random.seed[1]),
-  glmnet_model(lambda = 0.5, alpha = 0)
+    exper,
+    lnm_model(seed = .Random.seed[1]),
+    glmnet_model(lambda = 0.5, alpha = 0)
 ) |>
-  estimate(exper)
+ estimate(exper) 
#> ------------------------------------------------------------ 
 #> EXPERIMENTAL ALGORITHM: 
 #>   This procedure has not been thoroughly tested and may be unstable 
 #>   or buggy. The interface is subject to change. 
 #> ------------------------------------------------------------ 
-#> Gradient evaluation took 0.008748 seconds 
-#> 1000 transitions using 10 leapfrog steps per transition would take 87.48 seconds. 
+#> Gradient evaluation took 0.011177 seconds 
+#> 1000 transitions using 10 leapfrog steps per transition would take 111.77 seconds. 
 #> Adjust your expectations accordingly! 
 #> Begin eta adaptation. 
 #> Iteration:   1 / 250 [  0%]  (Adaptation) 
@@ -195,7 +195,7 @@ 
The Mindfulness Study

 #>   1300       -83647.463             0.016            0.008   MEDIAN ELBO CONVERGED 
 #> Drawing a sample of size 1000 from the approximate posterior...  
 #> COMPLETED. 
-#> Finished in  15.3 seconds.
+#> Finished in 15.1 seconds.

Evaluating Effects

@@ -206,9 +206,9 @@

Evaluating Effects
 direct <- direct_effect(model, exper)
 direct |>
-  group_by(outcome) |>
-  summarise(direct_effect = mean(direct_effect)) |>
-  arrange(-abs(direct_effect))

+ group_by(outcome) |> + summarise(direct_effect = mean(direct_effect)) |> + arrange(-abs(direct_effect)) 
#> # A tibble: 55 × 2
 #>    outcome          direct_effect
 #>                        
@@ -227,9 +227,9 @@ 
Evaluating Effects
 indirect <- indirect_pathwise(model, exper) |>
-  group_by(mediator, outcome) |>
-  summarise(indirect_effect = mean(indirect_effect)) |>
-  arrange(-abs(indirect_effect))
+    group_by(mediator, outcome) |>
+    summarise(indirect_effect = mean(indirect_effect)) |>
+    arrange(-abs(indirect_effect))
 indirect

 
#> # A tibble: 220 × 3
 #> # Groups:   mediator [4]
@@ -273,15 +273,15 @@ 
Model Alterations
 altered <- model |>
-  nullify("T->M") |>
-  estimate(exper)

+    nullify("T->M") |>
+    estimate(exper)

 
#> ------------------------------------------------------------ 
 #> EXPERIMENTAL ALGORITHM: 
 #>   This procedure has not been thoroughly tested and may be unstable 
 #>   or buggy. The interface is subject to change. 
 #> ------------------------------------------------------------ 
-#> Gradient evaluation took 0.009652 seconds 
-#> 1000 transitions using 10 leapfrog steps per transition would take 96.52 seconds. 
+#> Gradient evaluation took 0.010854 seconds 
+#> 1000 transitions using 10 leapfrog steps per transition would take 108.54 seconds. 
 #> Adjust your expectations accordingly! 
 #> Begin eta adaptation. 
 #> Iteration:   1 / 250 [  0%]  (Adaptation) 
@@ -307,7 +307,7 @@ 
Model Alterations#>   1300       -83647.463             0.016            0.008   MEDIAN ELBO CONVERGED 
 #> Drawing a sample of size 1000 from the approximate posterior...  
 #> COMPLETED. 
-#> Finished in  14.9 seconds.

+#> Finished in  16.8 seconds.

These modified models can be used to simulate synthetic null data that help contextualize the effects seen in real data. For example, we can compare imaginary cohort drawn from the original and the altered @@ -317,7 +317,7 @@

Model Alterations
-new_assign <- treatments(exper)[sample(nrow(treatments(exper))),, drop=FALSE]
+new_assign <- treatments(exper)[sample(nrow(treatments(exper))), , drop = FALSE]
 profile <- setup_profile(model, new_assign, new_assign)
 m1 <- sample(model, profile = profile, pretreatment = pretreatments(exper))
 m2 <- sample(altered, profile = profile, pretreatment = pretreatments(exper))
@@ -329,15 +329,17 @@

Model Alterations
 list(
-  real = bind_cols(treatments(exper), mediators(exper), pretreatments(exper)),
-  original = bind_cols(new_assign, mediators(m1), pretreatments(exper)),
-  altered = bind_cols(new_assign, mediators(m2), pretreatments(exper))
+    real = bind_cols(treatments(exper), mediators(exper), pretreatments(exper)),
+    original = bind_cols(new_assign, mediators(m1), pretreatments(exper)),
+    altered = bind_cols(new_assign, mediators(m2), pretreatments(exper))
 ) |>
-  bind_rows(.id = "source") |>
-  pivot_longer(starts_with("mediator"), names_to = "mediator") |>
-  ggplot() +
-  geom_boxplot(aes(value, reorder(mediator, value, median), fill = treatment)) +
-  facet_grid(~source)
+ bind_rows(.id = "source") |> + pivot_longer(starts_with("mediator"), names_to = "mediator") |> + ggplot() + + geom_boxplot( + aes(value, reorder(mediator, value, median), fill = treatment) + ) + + facet_grid(~source)

Here is the analogous alteration that removes all direct effects. The xx-axis @@ -351,15 +353,15 @@

Model Alterations
 altered_direct <- model |>
-  nullify("T->Y") |>
-  estimate(exper)
+ nullify("T->Y") |> + estimate(exper) 
#> ------------------------------------------------------------ 
 #> EXPERIMENTAL ALGORITHM: 
 #>   This procedure has not been thoroughly tested and may be unstable 
 #>   or buggy. The interface is subject to change. 
 #> ------------------------------------------------------------ 
-#> Gradient evaluation took 0.008821 seconds 
-#> 1000 transitions using 10 leapfrog steps per transition would take 88.21 seconds. 
+#> Gradient evaluation took 0.016047 seconds 
+#> 1000 transitions using 10 leapfrog steps per transition would take 160.47 seconds. 
 #> Adjust your expectations accordingly! 
 #> Begin eta adaptation. 
 #> Iteration:   1 / 250 [  0%]  (Adaptation) 
@@ -384,19 +386,19 @@ 
Model Alterations#>   1200       -83870.635             0.040            0.010   MEDIAN ELBO CONVERGED 
 #> Drawing a sample of size 1000 from the approximate posterior...  
 #> COMPLETED. 
-#> Finished in  14.4 seconds.
+#> Finished in 15.9 seconds. + nullify("M->Y") |> + estimate(exper) 
#> ------------------------------------------------------------ 
 #> EXPERIMENTAL ALGORITHM: 
 #>   This procedure has not been thoroughly tested and may be unstable 
 #>   or buggy. The interface is subject to change. 
 #> ------------------------------------------------------------ 
-#> Gradient evaluation took 0.00862 seconds 
-#> 1000 transitions using 10 leapfrog steps per transition would take 86.2 seconds. 
+#> Gradient evaluation took 0.010268 seconds 
+#> 1000 transitions using 10 leapfrog steps per transition would take 102.68 seconds. 
 #> Adjust your expectations accordingly! 
 #> Begin eta adaptation. 
 #> Iteration:   1 / 250 [  0%]  (Adaptation) 
@@ -421,56 +423,62 @@ 
Model Alterations#>   1200       -83009.099             0.018            0.007   MEDIAN ELBO CONVERGED 
 #> Drawing a sample of size 1000 from the approximate posterior...  
 #> COMPLETED. 
-#> Finished in  14.3 seconds.
+#> Finished in 15.6 seconds. 
 
 profile <- setup_profile(model, treatments(exper), treatments(exper))
 y1 <- sample(model, profile = profile, pretreatment = pretreatments(exper))
-y2 <- sample(altered_direct, profile = profile, pretreatment = pretreatments(exper))
-y3 <- sample(altered_indirect, profile = profile, pretreatment = pretreatments(exper))
+y2 <- sample( + altered_direct, + profile = profile, pretreatment = pretreatments(exper) +) +y3 <- sample( + altered_indirect, + profile = profile, pretreatment = pretreatments(exper) +) 
 taxa_order <- normalize(outcomes(exper)) |>
-  log() |>
-  apply(2, \(x) {
-    x[is.infinite(x)] <- NA
-    median(x, na.rm = TRUE)
-  }) |>
-  order()
+    log() |>
+    apply(2, \(x) {
+        x[is.infinite(x)] <- NA
+        median(x, na.rm = TRUE)
+    }) |>
+    order()
 
 combined_samples <- list(
-  "Original Data" = normalize(outcomes(exper)),
-  "Full Model" = normalize(outcomes(y1)),
-  "No Direct Effect" = normalize(outcomes(y2)),
-  "No Indirect Effect" = normalize(outcomes(y3))
+    "Original Data" = normalize(outcomes(exper)),
+    "Full Model" = normalize(outcomes(y1)),
+    "No Direct Effect" = normalize(outcomes(y2)),
+    "No Indirect Effect" = normalize(outcomes(y3))
 ) |>
-  bind_rows(.id = "source") |>
-  mutate(treatment = rep(treatments(exper)$treatment, 4)) |>
-  pivot_longer(colnames(outcomes(exper))) |>
-  mutate(name = factor(name, levels = colnames(outcomes(exper))[taxa_order]))
+    bind_rows(.id = "source") |>
+    mutate(treatment = rep(treatments(exper)$treatment, 4)) |>
+    pivot_longer(colnames(outcomes(exper))) |>
+    mutate(name = factor(name, levels = colnames(outcomes(exper))[taxa_order]))
 
 ggplot(combined_samples) +
-  geom_boxplot(
-    aes(log(value), name, fill = treatment),
-    size = 0.4, outlier.size = 0.8, position = "identity",
-    alpha = 0.7
-  ) +
-  labs(x = "log(Relative Abundance)", y = "Genus", fill = "", col = "") +
-  facet_grid(~source, scales = "free") +
-  theme(panel.border = element_rect(fill = NA))
+ geom_boxplot( + aes(log(value), name, fill = treatment), + size = 0.4, outlier.size = 0.8, position = "identity", + alpha = 0.7 + ) + + labs(x = "log(Relative Abundance)", y = "Genus", fill = "", col = "") + + facet_grid(~source, scales = "free") + + theme(panel.border = element_rect(fill = NA)) 

 combined_samples |>
-  group_by(name, source, treatment) |>
-  summarise(presence = mean(value > 0)) |>
-  ggplot() +
-  geom_col(
-    aes(presence, name, fill = treatment, col = treatment),
-    position = "identity", width = 1,
-    alpha = 0.7
-  ) +
-  facet_grid(~source, scales = "free") +
-  scale_x_continuous(expand = c(0, 0)) +
-  theme(panel.border = element_rect(fill = NA))
+ group_by(name, source, treatment) |> + summarise(presence = mean(value > 0)) |> + ggplot() + + geom_col( + aes(presence, name, fill = treatment, col = treatment), + position = "identity", width = 1, + alpha = 0.7 + ) + + facet_grid(~source, scales = "free") + + scale_x_continuous(expand = c(0, 0)) + + theme(panel.border = element_rect(fill = NA))

@@ -506,8 +514,8 @@

Synthetic Null Testing#> This procedure has not been thoroughly tested and may be unstable #> or buggy. The interface is subject to change. #> ------------------------------------------------------------ -#> Gradient evaluation took 0.009921 seconds -#> 1000 transitions using 10 leapfrog steps per transition would take 99.21 seconds. +#> Gradient evaluation took 0.008489 seconds +#> 1000 transitions using 10 leapfrog steps per transition would take 84.89 seconds. #> Adjust your expectations accordingly! #> Begin eta adaptation. #> Iteration: 1 / 250 [ 0%] (Adaptation) @@ -532,14 +540,14 @@

Synthetic Null Testing#> 1200 -83870.635 0.040 0.010 MEDIAN ELBO CONVERGED #> Drawing a sample of size 1000 from the approximate posterior... #> COMPLETED. -#> Finished in 14.9 seconds. +#> Finished in 15.1 seconds. #> ------------------------------------------------------------ #> EXPERIMENTAL ALGORITHM: #> This procedure has not been thoroughly tested and may be unstable #> or buggy. The interface is subject to change. #> ------------------------------------------------------------ -#> Gradient evaluation took 0.007981 seconds -#> 1000 transitions using 10 leapfrog steps per transition would take 79.81 seconds. +#> Gradient evaluation took 0.00817 seconds +#> 1000 transitions using 10 leapfrog steps per transition would take 81.7 seconds. #> Adjust your expectations accordingly! #> Begin eta adaptation. #> Iteration: 1 / 250 [ 0%] (Adaptation) @@ -564,10 +572,10 @@

Synthetic Null Testing#> 1200 -93959.448 0.051 0.010 MEDIAN ELBO CONVERGED #> Drawing a sample of size 1000 from the approximate posterior... #> COMPLETED. -#> Finished in 13.7 seconds. +#> Finished in 14.5 seconds. 
 fdr_direct <- fdr_summary(contrast, "direct_effect") |>
-  dplyr::rename(effect = direct_effect)
+ dplyr::rename(effect = direct_effect)

The indirect effect analog is shown below. It seems we have more evidence for direct than indirect effects. This is consistent with literature on the difficulty of estimating indirect effects in mediation @@ -579,8 +587,8 @@

Synthetic Null Testing#> This procedure has not been thoroughly tested and may be unstable #> or buggy. The interface is subject to change. #> ------------------------------------------------------------ -#> Gradient evaluation took 0.009195 seconds -#> 1000 transitions using 10 leapfrog steps per transition would take 91.95 seconds. +#> Gradient evaluation took 0.007982 seconds +#> 1000 transitions using 10 leapfrog steps per transition would take 79.82 seconds. #> Adjust your expectations accordingly! #> Begin eta adaptation. #> Iteration: 1 / 250 [ 0%] (Adaptation) @@ -605,14 +613,14 @@

Synthetic Null Testing#> 1200 -83009.099 0.018 0.007 MEDIAN ELBO CONVERGED #> Drawing a sample of size 1000 from the approximate posterior... #> COMPLETED. -#> Finished in 15.7 seconds. +#> Finished in 14.3 seconds. #> ------------------------------------------------------------ #> EXPERIMENTAL ALGORITHM: #> This procedure has not been thoroughly tested and may be unstable #> or buggy. The interface is subject to change. #> ------------------------------------------------------------ -#> Gradient evaluation took 0.008695 seconds -#> 1000 transitions using 10 leapfrog steps per transition would take 86.95 seconds. +#> Gradient evaluation took 0.008389 seconds +#> 1000 transitions using 10 leapfrog steps per transition would take 83.89 seconds. #> Adjust your expectations accordingly! #> Begin eta adaptation. #> Iteration: 1 / 250 [ 0%] (Adaptation) @@ -639,46 +647,55 @@

Synthetic Null Testing#> 1400 -92232.072 0.019 0.006 MEDIAN ELBO CONVERGED #> Drawing a sample of size 1000 from the approximate posterior... #> COMPLETED. -#> Finished in 17.2 seconds. +#> Finished in 16.2 seconds. 
 fdr_indirect <- fdr_summary(contrast, "indirect_overall") |>
-  dplyr::rename(effect = indirect_effect)
+ dplyr::rename(effect = indirect_effect) 
 fdr_data <- bind_rows(fdr_direct, fdr_indirect, .id = "effect_type") |>
-  mutate(effect_type = c("Direct", "Indirect")[as.integer(effect_type)])
+    mutate(effect_type = c("Direct", "Indirect")[as.integer(effect_type)])
 ggplot(fdr_data, aes(effect, fdr_hat)) +
-  geom_text_repel(data = filter(fdr_data, keep), aes(label = outcome, col = source), size = 3, force = 10) +
-  labs(x = "Effect", y = expression(widehat(FDR)), col = "Data Source") +
-  geom_point(aes(col = source, size = keep)) +
-  scale_size_discrete("Selected", range = c(.5, 3), guide = FALSE) +
-  scale_y_continuous(limits = c(-0.1, 0.55)) +
-  facet_wrap(~effect_type, scales = "free_x") +
-  theme(
-    axis.text.x = element_text(size = 12),
-    axis.text.y = element_text(size = 12),
-    strip.text = element_text(size = 14),
-    legend.text = element_text(size = 12)
-  )
+ geom_text_repel( + data = filter(fdr_data, keep), + aes(label = outcome, col = source), size = 3, force = 10 + ) + + labs(x = "Effect", y = expression(widehat(FDR)), col = "Data Source") + + geom_point(aes(col = source, size = keep)) + + scale_size_discrete("Selected", range = c(.5, 3), guide = FALSE) + + scale_y_continuous(limits = c(-0.1, 0.55)) + + facet_wrap(~effect_type, scales = "free_x") + + theme( + axis.text.x = element_text(size = 12), + axis.text.y = element_text(size = 12), + strip.text = element_text(size = 14), + legend.text = element_text(size = 12) + ) 

 bind_mediation(exper_rela) |>
-  select(subject, starts_with("mediator"), treatment, Roseburia, Blautia, Faecalibacterium) |>
-  pivot_longer(starts_with("mediator"), names_to = "mediator") |>
-  mutate(mediator = str_remove(mediator, "mediator.")) |>
-  pivot_longer(Roseburia:Faecalibacterium, names_to = "taxon", values_to = "abundance") |>
-  group_by(subject, mediator, treatment, taxon) |>
-  summarise(abundance = mean(abundance), value = mean(value)) |>
-  ggplot() +
-  geom_point(aes(value, abundance, col = treatment)) +
-  facet_grid(taxon ~ mediator, scales = "free") +
-  labs(y = "Relative Abundance", x = "Mediator Value", col = "") +
-  theme(
-    axis.title = element_text(size = 14),
-    strip.text = element_text(size = 12),
-    strip.text.y = element_text(size = 12, angle = 0),
-    legend.text = element_text(size = 12),
-    panel.border = element_rect(fill = NA)
-  )
+ select( + subject, starts_with("mediator"), treatment, Roseburia, Blautia, + Faecalibacterium + ) |> + pivot_longer(starts_with("mediator"), names_to = "mediator") |> + mutate(mediator = str_remove(mediator, "mediator.")) |> + pivot_longer( + Roseburia:Faecalibacterium, + names_to = "taxon", values_to = "abundance" + ) |> + group_by(subject, mediator, treatment, taxon) |> + summarise(abundance = mean(abundance), value = mean(value)) |> + ggplot() + + geom_point(aes(value, abundance, col = treatment)) + + facet_grid(taxon ~ mediator, scales = "free") + + labs(y = "Relative Abundance", x = "Mediator Value", col = "") + + theme( + axis.title = element_text(size = 14), + strip.text = element_text(size = 12), + strip.text.y = element_text(size = 12, angle = 0), + legend.text = element_text(size = 12), + panel.border = element_rect(fill = NA) + )

Here is the analog for indirect pathwise effects. Since these effects distinguish between individual mediators, we can facet by these @@ -690,8 +707,8 @@

Synthetic Null Testing#> This procedure has not been thoroughly tested and may be unstable #> or buggy. The interface is subject to change. #> ------------------------------------------------------------ -#> Gradient evaluation took 0.007716 seconds -#> 1000 transitions using 10 leapfrog steps per transition would take 77.16 seconds. +#> Gradient evaluation took 0.00768 seconds +#> 1000 transitions using 10 leapfrog steps per transition would take 76.8 seconds. #> Adjust your expectations accordingly! #> Begin eta adaptation. #> Iteration: 1 / 250 [ 0%] (Adaptation) @@ -716,14 +733,14 @@

Synthetic Null Testing#> 1200 -83009.099 0.018 0.007 MEDIAN ELBO CONVERGED #> Drawing a sample of size 1000 from the approximate posterior... #> COMPLETED. -#> Finished in 13.4 seconds. +#> Finished in 13.9 seconds. #> ------------------------------------------------------------ #> EXPERIMENTAL ALGORITHM: #> This procedure has not been thoroughly tested and may be unstable #> or buggy. The interface is subject to change. #> ------------------------------------------------------------ -#> Gradient evaluation took 0.008217 seconds -#> 1000 transitions using 10 leapfrog steps per transition would take 82.17 seconds. +#> Gradient evaluation took 0.008923 seconds +#> 1000 transitions using 10 leapfrog steps per transition would take 89.23 seconds. #> Adjust your expectations accordingly! #> Begin eta adaptation. #> Iteration: 1 / 250 [ 0%] (Adaptation) @@ -749,15 +766,18 @@

Synthetic Null Testing#> 1300 -92870.784 0.015 0.008 MEDIAN ELBO CONVERGED #> Drawing a sample of size 1000 from the approximate posterior... #> COMPLETED. -#> Finished in 13.4 seconds. +#> Finished in 15.1 seconds. 
 fdr <- fdr_summary(contrast, "indirect_pathwise")
 ggplot(fdr, aes(indirect_effect, fdr_hat)) +
-  geom_text_repel(data = filter(fdr, keep), aes(label = outcome, fill = source), size = 4) +
-  labs(x = "Indirect Effect", y = "Estimated False Discovery Rate") +
-  geom_point(aes(col = source, size = keep)) +
-  scale_size_discrete(range = c(.2, 3)) +
-  facet_wrap(~mediator)
+ geom_text_repel( + data = filter(fdr, keep), + aes(label = outcome, fill = source), size = 4 + ) + + labs(x = "Indirect Effect", y = "Estimated False Discovery Rate") + + geom_point(aes(col = source, size = keep)) + + scale_size_discrete(range = c(.2, 3)) + + facet_wrap(~mediator)

@@ -771,24 +791,24 @@

Random Forests 
 model <- multimedia(
-  exper_rela,
-  rf_model(num.trees = 50),
-  glmnet_model(lambda = 0.5, alpha = 0)
+    exper_rela,
+    rf_model(num.trees = 50),
+    glmnet_model(lambda = 0.5, alpha = 0)
 ) |>
-  estimate(exper_rela)
+ estimate(exper_rela)

We can compute direct and indirect effects from the estimated model.

 direct <- direct_effect(model, exper_rela)
 direct_sorted <- direct |>
-  group_by(outcome, contrast) |>
-  summarise(direct_effect = mean(direct_effect)) |>
-  arrange(-direct_effect)
+    group_by(outcome, contrast) |>
+    summarise(direct_effect = mean(direct_effect)) |>
+    arrange(-direct_effect)
 
 indirect_sorted <- indirect_pathwise(model, exper_rela) |>
-  group_by(outcome, mediator, contrast) |>
-  summarise(indirect_effect = mean(indirect_effect)) |>
-  arrange(-abs(indirect_effect))
+    group_by(outcome, mediator, contrast) |>
+    summarise(indirect_effect = mean(indirect_effect)) |>
+    arrange(-abs(indirect_effect))
 
 direct_sorted
#> # A tibble: 55 × 3
@@ -842,8 +862,8 @@ 
Bootstrap
 funs <- list(direct = direct_effect, indirect = indirect_overall)
-#inference <- bootstrap(model, exper_rela, funs, B = 1e3)
-inference <- readRDS(url("https://drive.google.com/uc?export=download&id=196yFXbuyeZShpZr58WZpUI3EEArotMuk"))

+# inference <- bootstrap(model, exper_rela, funs, B = 1e3)
+inference <- readRDS(url("https://go.wisc.edu/ba3e87"))

We can now visualize the bootstrap confidence intervals associated with the estimated effects. The largest interval corresponds to a 90% bootstrap confidence interval. The inner interval covers the median +/- @@ -858,20 +878,22 @@

Bootstrap
 p1 <- ggplot(inference$indirect) +
-  geom_vline(xintercept = 0) +
-  stat_slabinterval(
-    aes(indirect_effect, reorder(outcome, indirect_effect, median)),
-    .width = c(.66, .95)
-  ) +
-  labs(title = "Indirect Effects", y = "Taxon", x = "Effect (Rel. Abund Scale)")
+    geom_vline(xintercept = 0) +
+    stat_slabinterval(
+        aes(indirect_effect, reorder(outcome, indirect_effect, median)),
+        .width = c(.66, .95)
+    ) +
+    labs(
+        title = "Indirect Effects", y = "Taxon", x = "Effect (Rel. Abund Scale)"
+    )
 
 p2 <- ggplot(inference$direct) +
-  geom_vline(xintercept = 0) +
-  stat_slabinterval(
-    aes(direct_effect, reorder(outcome, direct_effect, median)),
-    .width = c(.66, .95)
-  ) +
-  labs(title = "Direct Effects", y = "Taxon", x = "Effect (Rel. Abund Scale)")
+    geom_vline(xintercept = 0) +
+    stat_slabinterval(
+        aes(direct_effect, reorder(outcome, direct_effect, median)),
+        .width = c(.66, .95)
+    ) +
+    labs(title = "Direct Effects", y = "Taxon", x = "Effect (Rel. Abund Scale)")
 
 p1 | p2

@@ -928,7 +950,7 @@

Bootstrap#> [43] jquerylib_0.1.4 Rcpp_1.0.13 bookdown_0.40 #> [46] iterators_1.0.14 knitr_1.48 timechange_0.3.0 #> [49] Matrix_1.7-0 splines_4.4.1 igraph_2.0.3 -#> [52] abind_1.4-5 yaml_2.3.10 vegan_2.6-6.1 +#> [52] abind_1.4-5 yaml_2.3.10 vegan_2.6-8 #> [55] codetools_0.2-20 processx_3.8.4 lattice_0.22-6 #> [58] plyr_1.8.9 withr_3.0.1 posterior_1.6.0 #> [61] evaluate_0.24.0 desc_1.4.3 survival_3.7-0 diff --git a/docs/articles/random.html b/docs/articles/random.html index 2757b57..3358a9c 100644 --- a/docs/articles/random.html +++ b/docs/articles/random.html @@ -18,15 +18,13 @@ - - - +
@@ -79,7 +87,7 @@ - +
@@ -87,7 +95,7 @@

Quick Start with Random Data

- + Source: vignettes/random.Rmd
@@ -95,8 +103,8 @@

Quick Start with Random Data

This vignette gives a brief introduction using simulated that resemble a mediation analysis of the gut-brain axis. The basic question @@ -129,7 +137,7 @@

Quick Start with Random Data

linear regression model for each mediation and outcome variable.

 model <- multimedia(exper) |>
-  estimate(exper)
+    estimate(exper)
 
 model
#> [Multimedia Analysis] 
@@ -140,13 +148,14 @@ 
Quick Start with Random Data

 #> [Models] 
 #> mediation: A fitted lm_model(). 
 #> outcome: A fitted lm_model().
-

The edges slot tracks all the variable relationships. -For example, we can visualize the causal graph using the -ggraph code below.

+

The edges slot tracks all the variable relationships, +and it can be accessed using the edges method. For example, +we can visualize the causal graph using the ggraph code +below.

-ggraph(model@edges) +
-  geom_edge_link(arrow = arrow()) +
-  geom_node_label(aes(label = name, fill = node_type))
+ggraph(edges(model)) + + geom_edge_link(arrow = arrow()) + + geom_node_label(aes(label = name, fill = node_type))

Now that we’ve coupled the mediation and outcome models, we can propogate predictions and samples through them. That is, we can define @@ -186,8 +195,9 @@

Quick Start with Random Data

with this kind of configuration and three others that keep all edges at control.

-t_mediator <- model@treatments[c(2, rep(1, 3)),, drop=FALSE]
-t_outcome <- model@treatments[rep(1, 4),, drop=FALSE]
+t_mediator <- factor(c("Treatment", rep("Control", 3)))
+t_outcome <- factor(rep("Control", 4), levels = c("Treatment", "Control"))
+
 profile <- setup_profile(model, t_mediator, t_outcome)
 sample(model, profile = profile)
#> [Mediation Data] 
@@ -214,10 +224,58 @@ 
Quick Start with Random Data

 #> 2 -0.129
 #> 3 -0.129
 #> 4 -0.129
+
+
+setup_profile(model, t_mediator, t_outcome)
+
#> An object of class "treatment_profile"
+#> Slot "t_mediator":
+#> $ASV1
+#>   treatment
+#> 1 Treatment
+#> 2   Control
+#> 3   Control
+#> 4   Control
+#> 
+#> $ASV2
+#>   treatment
+#> 1 Treatment
+#> 2   Control
+#> 3   Control
+#> 4   Control
+#> 
+#> $ASV3
+#>   treatment
+#> 1 Treatment
+#> 2   Control
+#> 3   Control
+#> 4   Control
+#> 
+#> $ASV4
+#>   treatment
+#> 1 Treatment
+#> 2   Control
+#> 3   Control
+#> 4   Control
+#> 
+#> $ASV5
+#>   treatment
+#> 1 Treatment
+#> 2   Control
+#> 3   Control
+#> 4   Control
+#> 
+#> 
+#> Slot "t_outcome":
+#> $PHQ
+#>   treatment
+#> 1   Control
+#> 2   Control
+#> 3   Control
+#> 4   Control

We can also contrast the predictions and samples under different profiles.

-
-profile_control <- setup_profile(model, model@treatments[rep(1, 4),, drop = FALSE], t_outcome)
+
+profile_control <- setup_profile(model, t_outcome, t_outcome)
 contrast_predictions(model, profile, profile_control)

 
#> $mediators
 #>          ASV1      ASV2      ASV3      ASV4        ASV5
@@ -232,7 +290,7 @@ 
Quick Start with Random Data

 #> 2  0.000000000
 #> 3  0.000000000
 #> 4  0.000000000

-
+
 contrast_samples(model, profile, profile_control)

 
#> $mediators
 #>         ASV1        ASV2       ASV3       ASV4       ASV5
@@ -252,26 +310,29 @@ 
Effect Estimates
 
It’s a small step from contrasting different configurations to asking
 for the direct and indirect treatments effects. The direct effect is
-defined as the average of \(\hat{Y}\left(\hat{M}\left(t'\right), 1\right)
-- \hat{Y}\left(\hat{M}\left(t'\right), 0\right)\) across
-mediator treatment effects \(t'\).
+defined as the average of
+Ŷ(M̂(t′),1)−Ŷ(M̂(t′),0)
+\hat{Y}\left(\hat{M}\left(t'\right), 1\right) -  
+\hat{Y}\left(\hat{M}\left(t'\right), 0\right)
+ across mediator treatment effects
+t′t'.
 The hats mean that we use the predicted values from the mediation and
 outcome values. I’ve distinguished between “overall” and “pathwise”
 indirect effects because we’re working with high-dimensional mediators.
 In the overall effect, we toggle treatment/control status for incoming
 edges to all mediators. In pathwise indirect effects, we toggle only the
 treatment going into one mediator.

-
+
 direct_effect(model, exper)

 
#>   outcome indirect_setting            contrast direct_effect
 #> 1     PHQ          Control Control - Treatment   -0.08646108
 #> 2     PHQ        Treatment Control - Treatment   -0.08646108

-
+
 indirect_overall(model, exper)

 
#>   outcome direct_setting            contrast indirect_effect
 #> 1     PHQ        Control Control - Treatment     0.004711189
 #> 2     PHQ      Treatment Control - Treatment     0.004711189

-
+
 indirect_pathwise(model, exper)

 
#>    outcome mediator direct_setting            contrast indirect_effect
 #> 1      PHQ     ASV1        Control Control - Treatment     0.002020718
@@ -294,20 +355,20 @@ 
Effect Estimates
-
+
 model <- multimedia(exper, glmnet_model(lambda = .1)) |>
-  estimate(exper)
+    estimate(exper)
 
 direct_effect(model, exper)

 
#>   outcome indirect_setting            contrast direct_effect
 #> 1     PHQ          Control Control - Treatment   -0.05366268
 #> 2     PHQ        Treatment Control - Treatment   -0.05366268

-
+
 indirect_overall(model, exper)

 
#>   outcome direct_setting            contrast indirect_effect
 #> 1     PHQ        Control Control - Treatment      0.01384187
 #> 2     PHQ      Treatment Control - Treatment      0.01384187

-
+
 indirect_pathwise(model, exper)

 
#>    outcome mediator direct_setting            contrast indirect_effect
 #> 1      PHQ     ASV1        Control Control - Treatment     0.000000000
@@ -329,2010 +390,20 @@ 
Inference
-bootstrap(model, exper, c(direct_effect = direct_effect))

-
#> $direct_effect
-#>      bootstrap outcome indirect_setting            contrast direct_effect
-#> 1            1     PHQ          Control Control - Treatment -7.762666e-02
-#> 2            1     PHQ        Treatment Control - Treatment -7.762666e-02
-#> 3            2     PHQ          Control Control - Treatment -1.324763e-01
-#> 4            2     PHQ        Treatment Control - Treatment -1.324763e-01
-#> 5            3     PHQ          Control Control - Treatment -8.455178e-02
-#> 6            3     PHQ        Treatment Control - Treatment -8.455178e-02
-#> 7            4     PHQ          Control Control - Treatment -1.042292e-01
-#> 8            4     PHQ        Treatment Control - Treatment -1.042292e-01
-#> 9            5     PHQ          Control Control - Treatment -1.521041e-01
-#> 10           5     PHQ        Treatment Control - Treatment -1.521041e-01
-#> 11           6     PHQ          Control Control - Treatment -1.187328e-01
-#> 12           6     PHQ        Treatment Control - Treatment -1.187328e-01
-#> 13           7     PHQ          Control Control - Treatment -1.567047e-01
-#> 14           7     PHQ        Treatment Control - Treatment -1.567047e-01
-#> 15           8     PHQ          Control Control - Treatment  9.642162e-02
-#> 16           8     PHQ        Treatment Control - Treatment  9.642162e-02
-#> 17           9     PHQ          Control Control - Treatment -1.438649e-01
-#> 18           9     PHQ        Treatment Control - Treatment -1.438649e-01
-#> 19          10     PHQ          Control Control - Treatment -4.427735e-02
-#> 20          10     PHQ        Treatment Control - Treatment -4.427735e-02
-#> 21          11     PHQ          Control Control - Treatment -2.322077e-01
-#> 22          11     PHQ        Treatment Control - Treatment -2.322077e-01
-#> 23          12     PHQ          Control Control - Treatment  3.484604e-02
-#> 24          12     PHQ        Treatment Control - Treatment  3.484604e-02
-#> 25          13     PHQ          Control Control - Treatment -2.368980e-01
-#> 26          13     PHQ        Treatment Control - Treatment -2.368980e-01
-#> 27          14     PHQ          Control Control - Treatment -3.304762e-01
-#> 28          14     PHQ        Treatment Control - Treatment -3.304762e-01
-#> 29          15     PHQ          Control Control - Treatment -1.025688e-01
-#> 30          15     PHQ        Treatment Control - Treatment -1.025688e-01
-#> 31          16     PHQ          Control Control - Treatment  0.000000e+00
-#> 32          16     PHQ        Treatment Control - Treatment  0.000000e+00
-#> 33          17     PHQ          Control Control - Treatment -1.837012e-02
-#> 34          17     PHQ        Treatment Control - Treatment -1.837012e-02
-#> 35          18     PHQ          Control Control - Treatment -1.666047e-01
-#> 36          18     PHQ        Treatment Control - Treatment -1.666047e-01
-#> 37          19     PHQ          Control Control - Treatment  9.319094e-02
-#> 38          19     PHQ        Treatment Control - Treatment  9.319094e-02
-#> 39          20     PHQ          Control Control - Treatment -1.310074e-01
-#> 40          20     PHQ        Treatment Control - Treatment -1.310074e-01
-#> 41          21     PHQ          Control Control - Treatment -1.073142e-01
-#> 42          21     PHQ        Treatment Control - Treatment -1.073142e-01
-#> 43          22     PHQ          Control Control - Treatment -7.778502e-02
-#> 44          22     PHQ        Treatment Control - Treatment -7.778502e-02
-#> 45          23     PHQ          Control Control - Treatment -1.557000e-02
-#> 46          23     PHQ        Treatment Control - Treatment -1.557000e-02
-#> 47          24     PHQ          Control Control - Treatment  3.432699e-03
-#> 48          24     PHQ        Treatment Control - Treatment  3.432699e-03
-#> 49          25     PHQ          Control Control - Treatment  5.457910e-03
-#> 50          25     PHQ        Treatment Control - Treatment  5.457910e-03
-#> 51          26     PHQ          Control Control - Treatment -6.537745e-02
-#> 52          26     PHQ        Treatment Control - Treatment -6.537745e-02
-#> 53          27     PHQ          Control Control - Treatment -1.032590e-01
-#> 54          27     PHQ        Treatment Control - Treatment -1.032590e-01
-#> 55          28     PHQ          Control Control - Treatment -1.017752e-01
-#> 56          28     PHQ        Treatment Control - Treatment -1.017752e-01
-#> 57          29     PHQ          Control Control - Treatment  1.416466e-02
-#> 58          29     PHQ        Treatment Control - Treatment  1.416466e-02
-#> 59          30     PHQ          Control Control - Treatment  0.000000e+00
-#> 60          30     PHQ        Treatment Control - Treatment  0.000000e+00
-#> 61          31     PHQ          Control Control - Treatment -8.061846e-03
-#> 62          31     PHQ        Treatment Control - Treatment -8.061846e-03
-#> 63          32     PHQ          Control Control - Treatment -9.446516e-02
-#> 64          32     PHQ        Treatment Control - Treatment -9.446516e-02
-#> 65          33     PHQ          Control Control - Treatment  6.297865e-02
-#> 66          33     PHQ        Treatment Control - Treatment  6.297865e-02
-#> 67          34     PHQ          Control Control - Treatment -9.254250e-02
-#> 68          34     PHQ        Treatment Control - Treatment -9.254250e-02
-#> 69          35     PHQ          Control Control - Treatment  0.000000e+00
-#> 70          35     PHQ        Treatment Control - Treatment  0.000000e+00
-#> 71          36     PHQ          Control Control - Treatment -8.402947e-02
-#> 72          36     PHQ        Treatment Control - Treatment -8.402947e-02
-#> 73          37     PHQ          Control Control - Treatment -1.930173e-01
-#> 74          37     PHQ        Treatment Control - Treatment -1.930173e-01
-#> 75          38     PHQ          Control Control - Treatment -2.220973e-01
-#> 76          38     PHQ        Treatment Control - Treatment -2.220973e-01
-#> 77          39     PHQ          Control Control - Treatment  2.848019e-02
-#> 78          39     PHQ        Treatment Control - Treatment  2.848019e-02
-#> 79          40     PHQ          Control Control - Treatment -3.070817e-01
-#> 80          40     PHQ        Treatment Control - Treatment -3.070817e-01
-#> 81          41     PHQ          Control Control - Treatment  0.000000e+00
-#> 82          41     PHQ        Treatment Control - Treatment  0.000000e+00
-#> 83          42     PHQ          Control Control - Treatment -1.006393e-01
-#> 84          42     PHQ        Treatment Control - Treatment -1.006393e-01
-#> 85          43     PHQ          Control Control - Treatment  1.919206e-01
-#> 86          43     PHQ        Treatment Control - Treatment  1.919206e-01
-#> 87          44     PHQ          Control Control - Treatment  2.539128e-02
-#> 88          44     PHQ        Treatment Control - Treatment  2.539128e-02
-#> 89          45     PHQ          Control Control - Treatment  1.231050e-03
-#> 90          45     PHQ        Treatment Control - Treatment  1.231050e-03
-#> 91          46     PHQ          Control Control - Treatment  0.000000e+00
-#> 92          46     PHQ        Treatment Control - Treatment  0.000000e+00
-#> 93          47     PHQ          Control Control - Treatment -7.170489e-02
-#> 94          47     PHQ        Treatment Control - Treatment -7.170489e-02
-#> 95          48     PHQ          Control Control - Treatment -2.898635e-01
-#> 96          48     PHQ        Treatment Control - Treatment -2.898635e-01
-#> 97          49     PHQ          Control Control - Treatment  5.756366e-02
-#> 98          49     PHQ        Treatment Control - Treatment  5.756366e-02
-#> 99          50     PHQ          Control Control - Treatment  0.000000e+00
-#> 100         50     PHQ        Treatment Control - Treatment  0.000000e+00
-#> 101         51     PHQ          Control Control - Treatment -2.082641e-01
-#> 102         51     PHQ        Treatment Control - Treatment -2.082641e-01
-#> 103         52     PHQ          Control Control - Treatment -2.994597e-02
-#> 104         52     PHQ        Treatment Control - Treatment -2.994597e-02
-#> 105         53     PHQ          Control Control - Treatment -1.627506e-02
-#> 106         53     PHQ        Treatment Control - Treatment -1.627506e-02
-#> 107         54     PHQ          Control Control - Treatment -3.293532e-01
-#> 108         54     PHQ        Treatment Control - Treatment -3.293532e-01
-#> 109         55     PHQ          Control Control - Treatment  0.000000e+00
-#> 110         55     PHQ        Treatment Control - Treatment  0.000000e+00
-#> 111         56     PHQ          Control Control - Treatment  1.170738e-01
-#> 112         56     PHQ        Treatment Control - Treatment  1.170738e-01
-#> 113         57     PHQ          Control Control - Treatment -2.275115e-01
-#> 114         57     PHQ        Treatment Control - Treatment -2.275115e-01
-#> 115         58     PHQ          Control Control - Treatment -1.004455e-01
-#> 116         58     PHQ        Treatment Control - Treatment -1.004455e-01
-#> 117         59     PHQ          Control Control - Treatment  2.414521e-02
-#> 118         59     PHQ        Treatment Control - Treatment  2.414521e-02
-#> 119         60     PHQ          Control Control - Treatment -2.181795e-01
-#> 120         60     PHQ        Treatment Control - Treatment -2.181795e-01
-#> 121         61     PHQ          Control Control - Treatment -1.061964e-01
-#> 122         61     PHQ        Treatment Control - Treatment -1.061964e-01
-#> 123         62     PHQ          Control Control - Treatment -5.863176e-02
-#> 124         62     PHQ        Treatment Control - Treatment -5.863176e-02
-#> 125         63     PHQ          Control Control - Treatment -1.437120e-01
-#> 126         63     PHQ        Treatment Control - Treatment -1.437120e-01
-#> 127         64     PHQ          Control Control - Treatment -8.816228e-02
-#> 128         64     PHQ        Treatment Control - Treatment -8.816228e-02
-#> 129         65     PHQ          Control Control - Treatment -2.636299e-01
-#> 130         65     PHQ        Treatment Control - Treatment -2.636299e-01
-#> 131         66     PHQ          Control Control - Treatment -6.887667e-02
-#> 132         66     PHQ        Treatment Control - Treatment -6.887667e-02
-#> 133         67     PHQ          Control Control - Treatment -1.801654e-02
-#> 134         67     PHQ        Treatment Control - Treatment -1.801654e-02
-#> 135         68     PHQ          Control Control - Treatment -1.821646e-02
-#> 136         68     PHQ        Treatment Control - Treatment -1.821646e-02
-#> 137         69     PHQ          Control Control - Treatment  1.738987e-02
-#> 138         69     PHQ        Treatment Control - Treatment  1.738987e-02
-#> 139         70     PHQ          Control Control - Treatment -4.716761e-02
-#> 140         70     PHQ        Treatment Control - Treatment -4.716761e-02
-#> 141         71     PHQ          Control Control - Treatment  0.000000e+00
-#> 142         71     PHQ        Treatment Control - Treatment  0.000000e+00
-#> 143         72     PHQ          Control Control - Treatment -1.611522e-02
-#> 144         72     PHQ        Treatment Control - Treatment -1.611522e-02
-#> 145         73     PHQ          Control Control - Treatment -4.055384e-02
-#> 146         73     PHQ        Treatment Control - Treatment -4.055384e-02
-#> 147         74     PHQ          Control Control - Treatment -9.743863e-03
-#> 148         74     PHQ        Treatment Control - Treatment -9.743863e-03
-#> 149         75     PHQ          Control Control - Treatment -9.652140e-02
-#> 150         75     PHQ        Treatment Control - Treatment -9.652140e-02
-#> 151         76     PHQ          Control Control - Treatment  3.002125e-02
-#> 152         76     PHQ        Treatment Control - Treatment  3.002125e-02
-#> 153         77     PHQ          Control Control - Treatment -1.483893e-01
-#> 154         77     PHQ        Treatment Control - Treatment -1.483893e-01
-#> 155         78     PHQ          Control Control - Treatment -1.561849e-01
-#> 156         78     PHQ        Treatment Control - Treatment -1.561849e-01
-#> 157         79     PHQ          Control Control - Treatment -2.649322e-01
-#> 158         79     PHQ        Treatment Control - Treatment -2.649322e-01
-#> 159         80     PHQ          Control Control - Treatment -9.521887e-02
-#> 160         80     PHQ        Treatment Control - Treatment -9.521887e-02
-#> 161         81     PHQ          Control Control - Treatment -8.667531e-02
-#> 162         81     PHQ        Treatment Control - Treatment -8.667531e-02
-#> 163         82     PHQ          Control Control - Treatment -2.534475e-02
-#> 164         82     PHQ        Treatment Control - Treatment -2.534475e-02
-#> 165         83     PHQ          Control Control - Treatment -6.987284e-03
-#> 166         83     PHQ        Treatment Control - Treatment -6.987284e-03
-#> 167         84     PHQ          Control Control - Treatment -1.061896e-01
-#> 168         84     PHQ        Treatment Control - Treatment -1.061896e-01
-#> 169         85     PHQ          Control Control - Treatment -2.272629e-01
-#> 170         85     PHQ        Treatment Control - Treatment -2.272629e-01
-#> 171         86     PHQ          Control Control - Treatment  0.000000e+00
-#> 172         86     PHQ        Treatment Control - Treatment  0.000000e+00
-#> 173         87     PHQ          Control Control - Treatment -1.177915e-01
-#> 174         87     PHQ        Treatment Control - Treatment -1.177915e-01
-#> 175         88     PHQ          Control Control - Treatment  0.000000e+00
-#> 176         88     PHQ        Treatment Control - Treatment  0.000000e+00
-#> 177         89     PHQ          Control Control - Treatment -2.166762e-01
-#> 178         89     PHQ        Treatment Control - Treatment -2.166762e-01
-#> 179         90     PHQ          Control Control - Treatment -9.250657e-02
-#> 180         90     PHQ        Treatment Control - Treatment -9.250657e-02
-#> 181         91     PHQ          Control Control - Treatment -7.273251e-02
-#> 182         91     PHQ        Treatment Control - Treatment -7.273251e-02
-#> 183         92     PHQ          Control Control - Treatment -1.658560e-01
-#> 184         92     PHQ        Treatment Control - Treatment -1.658560e-01
-#> 185         93     PHQ          Control Control - Treatment  0.000000e+00
-#> 186         93     PHQ        Treatment Control - Treatment  0.000000e+00
-#> 187         94     PHQ          Control Control - Treatment  1.938094e-03
-#> 188         94     PHQ        Treatment Control - Treatment  1.938094e-03
-#> 189         95     PHQ          Control Control - Treatment  3.216920e-01
-#> 190         95     PHQ        Treatment Control - Treatment  3.216920e-01
-#> 191         96     PHQ          Control Control - Treatment -8.174660e-02
-#> 192         96     PHQ        Treatment Control - Treatment -8.174660e-02
-#> 193         97     PHQ          Control Control - Treatment -1.038543e-01
-#> 194         97     PHQ        Treatment Control - Treatment -1.038543e-01
-#> 195         98     PHQ          Control Control - Treatment  1.381215e-01
-#> 196         98     PHQ        Treatment Control - Treatment  1.381215e-01
-#> 197         99     PHQ          Control Control - Treatment -1.703143e-01
-#> 198         99     PHQ        Treatment Control - Treatment -1.703143e-01
-#> 199        100     PHQ          Control Control - Treatment -2.691922e-02
-#> 200        100     PHQ        Treatment Control - Treatment -2.691922e-02
-#> 201        101     PHQ          Control Control - Treatment -1.652090e-01
-#> 202        101     PHQ        Treatment Control - Treatment -1.652090e-01
-#> 203        102     PHQ          Control Control - Treatment -4.783078e-02
-#> 204        102     PHQ        Treatment Control - Treatment -4.783078e-02
-#> 205        103     PHQ          Control Control - Treatment -1.430659e-02
-#> 206        103     PHQ        Treatment Control - Treatment -1.430659e-02
-#> 207        104     PHQ          Control Control - Treatment -8.269058e-02
-#> 208        104     PHQ        Treatment Control - Treatment -8.269058e-02
-#> 209        105     PHQ          Control Control - Treatment -1.188421e-01
-#> 210        105     PHQ        Treatment Control - Treatment -1.188421e-01
-#> 211        106     PHQ          Control Control - Treatment  8.680211e-02
-#> 212        106     PHQ        Treatment Control - Treatment  8.680211e-02
-#> 213        107     PHQ          Control Control - Treatment -5.092539e-02
-#> 214        107     PHQ        Treatment Control - Treatment -5.092539e-02
-#> 215        108     PHQ          Control Control - Treatment  0.000000e+00
-#> 216        108     PHQ        Treatment Control - Treatment  0.000000e+00
-#> 217        109     PHQ          Control Control - Treatment  4.745631e-02
-#> 218        109     PHQ        Treatment Control - Treatment  4.745631e-02
-#> 219        110     PHQ          Control Control - Treatment  0.000000e+00
-#> 220        110     PHQ        Treatment Control - Treatment  0.000000e+00
-#> 221        111     PHQ          Control Control - Treatment -1.190272e-01
-#> 222        111     PHQ        Treatment Control - Treatment -1.190272e-01
-#> 223        112     PHQ          Control Control - Treatment -1.524078e-01
-#> 224        112     PHQ        Treatment Control - Treatment -1.524078e-01
-#> 225        113     PHQ          Control Control - Treatment -1.096187e-01
-#> 226        113     PHQ        Treatment Control - Treatment -1.096187e-01
-#> 227        114     PHQ          Control Control - Treatment -6.831264e-02
-#> 228        114     PHQ        Treatment Control - Treatment -6.831264e-02
-#> 229        115     PHQ          Control Control - Treatment -1.332897e-01
-#> 230        115     PHQ        Treatment Control - Treatment -1.332897e-01
-#> 231        116     PHQ          Control Control - Treatment -3.052268e-02
-#> 232        116     PHQ        Treatment Control - Treatment -3.052268e-02
-#> 233        117     PHQ          Control Control - Treatment  0.000000e+00
-#> 234        117     PHQ        Treatment Control - Treatment  0.000000e+00
-#> 235        118     PHQ          Control Control - Treatment -1.451510e-01
-#> 236        118     PHQ        Treatment Control - Treatment -1.451510e-01
-#> 237        119     PHQ          Control Control - Treatment -2.066207e-01
-#> 238        119     PHQ        Treatment Control - Treatment -2.066207e-01
-#> 239        120     PHQ          Control Control - Treatment -1.209809e-01
-#> 240        120     PHQ        Treatment Control - Treatment -1.209809e-01
-#> 241        121     PHQ          Control Control - Treatment -8.028033e-02
-#> 242        121     PHQ        Treatment Control - Treatment -8.028033e-02
-#> 243        122     PHQ          Control Control - Treatment  1.333276e-01
-#> 244        122     PHQ        Treatment Control - Treatment  1.333276e-01
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-#> 249        125     PHQ          Control Control - Treatment  0.000000e+00
-#> 250        125     PHQ        Treatment Control - Treatment  0.000000e+00
-#> 251        126     PHQ          Control Control - Treatment -2.299748e-01
-#> 252        126     PHQ        Treatment Control - Treatment -2.299748e-01
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-#> 254        127     PHQ        Treatment Control - Treatment  0.000000e+00
-#> 255        128     PHQ          Control Control - Treatment  0.000000e+00
-#> 256        128     PHQ        Treatment Control - Treatment  0.000000e+00
-#> 257        129     PHQ          Control Control - Treatment -1.584480e-01
-#> 258        129     PHQ        Treatment Control - Treatment -1.584480e-01
-#> 259        130     PHQ          Control Control - Treatment  2.070209e-02
-#> 260        130     PHQ        Treatment Control - Treatment  2.070209e-02
-#> 261        131     PHQ          Control Control - Treatment  1.095261e-01
-#> 262        131     PHQ        Treatment Control - Treatment  1.095261e-01
-#> 263        132     PHQ          Control Control - Treatment -5.505505e-02
-#> 264        132     PHQ        Treatment Control - Treatment -5.505505e-02
-#> 265        133     PHQ          Control Control - Treatment -8.047061e-02
-#> 266        133     PHQ        Treatment Control - Treatment -8.047061e-02
-#> 267        134     PHQ          Control Control - Treatment -1.521274e-01
-#> 268        134     PHQ        Treatment Control - Treatment -1.521274e-01
-#> 269        135     PHQ          Control Control - Treatment -4.003398e-02
-#> 270        135     PHQ        Treatment Control - Treatment -4.003398e-02
-#> 271        136     PHQ          Control Control - Treatment  1.017973e-01
-#> 272        136     PHQ        Treatment Control - Treatment  1.017973e-01
-#> 273        137     PHQ          Control Control - Treatment -4.529145e-02
-#> 274        137     PHQ        Treatment Control - Treatment -4.529145e-02
-#> 275        138     PHQ          Control Control - Treatment -2.323296e-01
-#> 276        138     PHQ        Treatment Control - Treatment -2.323296e-01
-#> 277        139     PHQ          Control Control - Treatment  1.617812e-01
-#> 278        139     PHQ        Treatment Control - Treatment  1.617812e-01
-#> 279        140     PHQ          Control Control - Treatment -8.674083e-02
-#> 280        140     PHQ        Treatment Control - Treatment -8.674083e-02
-#> 281        141     PHQ          Control Control - Treatment -5.481912e-02
-#> 282        141     PHQ        Treatment Control - Treatment -5.481912e-02
-#> 283        142     PHQ          Control Control - Treatment  2.637698e-01
-#> 284        142     PHQ        Treatment Control - Treatment  2.637698e-01
-#> 285        143     PHQ          Control Control - Treatment -2.418545e-03
-#> 286        143     PHQ        Treatment Control - Treatment -2.418545e-03
-#> 287        144     PHQ          Control Control - Treatment -1.388641e-01
-#> 288        144     PHQ        Treatment Control - Treatment -1.388641e-01
-#> 289        145     PHQ          Control Control - Treatment -6.439074e-02
-#> 290        145     PHQ        Treatment Control - Treatment -6.439074e-02
-#> 291        146     PHQ          Control Control - Treatment -7.626521e-02
-#> 292        146     PHQ        Treatment Control - Treatment -7.626521e-02
-#> 293        147     PHQ          Control Control - Treatment -1.080242e-01
-#> 294        147     PHQ        Treatment Control - Treatment -1.080242e-01
-#> 295        148     PHQ          Control Control - Treatment -1.917407e-01
-#> 296        148     PHQ        Treatment Control - Treatment -1.917407e-01
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-#> 300        150     PHQ        Treatment Control - Treatment  2.920038e-03
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-#> 302        151     PHQ        Treatment Control - Treatment -1.141470e-01
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-#> 304        152     PHQ        Treatment Control - Treatment  1.069344e-02
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-#> 306        153     PHQ        Treatment Control - Treatment -1.167735e-01
-#> 307        154     PHQ          Control Control - Treatment -5.651319e-02
-#> 308        154     PHQ        Treatment Control - Treatment -5.651319e-02
-#> 309        155     PHQ          Control Control - Treatment -1.695445e-01
-#> 310        155     PHQ        Treatment Control - Treatment -1.695445e-01
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-#> 312        156     PHQ        Treatment Control - Treatment -2.327566e-01
-#> 313        157     PHQ          Control Control - Treatment -2.765415e-02
-#> 314        157     PHQ        Treatment Control - Treatment -2.765415e-02
-#> 315        158     PHQ          Control Control - Treatment -3.639388e-02
-#> 316        158     PHQ        Treatment Control - Treatment -3.639388e-02
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-#> 318        159     PHQ        Treatment Control - Treatment -2.444301e-01
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-#> 320        160     PHQ        Treatment Control - Treatment -9.933988e-02
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-#> 322        161     PHQ        Treatment Control - Treatment  7.410313e-03
-#> 323        162     PHQ          Control Control - Treatment -8.637349e-04
-#> 324        162     PHQ        Treatment Control - Treatment -8.637349e-04
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-#> 328        164     PHQ        Treatment Control - Treatment -1.472128e-01
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-#> 330        165     PHQ        Treatment Control - Treatment -8.406497e-03
-#> 331        166     PHQ          Control Control - Treatment -1.754614e-01
-#> 332        166     PHQ        Treatment Control - Treatment -1.754614e-01
-#> 333        167     PHQ          Control Control - Treatment -1.379040e-01
-#> 334        167     PHQ        Treatment Control - Treatment -1.379040e-01
-#> 335        168     PHQ          Control Control - Treatment -8.032566e-02
-#> 336        168     PHQ        Treatment Control - Treatment -8.032566e-02
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-#> 338        169     PHQ        Treatment Control - Treatment  1.181133e-01
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-#> 340        170     PHQ        Treatment Control - Treatment -1.721784e-01
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-#> 342        171     PHQ        Treatment Control - Treatment -4.776345e-02
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-#> 344        172     PHQ        Treatment Control - Treatment -1.442476e-02
-#> 345        173     PHQ          Control Control - Treatment  3.400862e-02
-#> 346        173     PHQ        Treatment Control - Treatment  3.400862e-02
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-#> 350        175     PHQ        Treatment Control - Treatment -2.576467e-01
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-#> 352        176     PHQ        Treatment Control - Treatment -1.282833e-02
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-#> 358        179     PHQ        Treatment Control - Treatment -4.737078e-02
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-#> 362        181     PHQ        Treatment Control - Treatment -2.698856e-02
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-#> 374        187     PHQ        Treatment Control - Treatment -1.859216e-01
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-#> 376        188     PHQ        Treatment Control - Treatment -2.145506e-02
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-#> 378        189     PHQ        Treatment Control - Treatment -1.890705e-01
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-#> 380        190     PHQ        Treatment Control - Treatment -4.877683e-02
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-#> 382        191     PHQ        Treatment Control - Treatment -2.370622e-01
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-#> 384        192     PHQ        Treatment Control - Treatment -4.820170e-02
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-#> 386        193     PHQ        Treatment Control - Treatment  1.708176e-01
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-#> 388        194     PHQ        Treatment Control - Treatment -1.666117e-01
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-#> 396        198     PHQ        Treatment Control - Treatment -1.752140e-01
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-#> 398        199     PHQ        Treatment Control - Treatment -2.064624e-02
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-#> 408        204     PHQ        Treatment Control - Treatment -1.407542e-01
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-#> 410        205     PHQ        Treatment Control - Treatment -6.302985e-02
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-#> 416        208     PHQ        Treatment Control - Treatment  8.038234e-03
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-#> 418        209     PHQ        Treatment Control - Treatment  2.483904e-02
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-#> 422        211     PHQ        Treatment Control - Treatment  5.454439e-02
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-#> 424        212     PHQ        Treatment Control - Treatment -1.271139e-01
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-#> 426        213     PHQ        Treatment Control - Treatment -6.954931e-02
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-#> 428        214     PHQ        Treatment Control - Treatment  2.411049e-02
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-#> 436        218     PHQ        Treatment Control - Treatment -4.809211e-02
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-#> 450        225     PHQ        Treatment Control - Treatment -2.169576e-01
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-#> 452        226     PHQ        Treatment Control - Treatment -8.365488e-02
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-#> 458        229     PHQ        Treatment Control - Treatment -7.798076e-02
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-#> 464        232     PHQ        Treatment Control - Treatment -6.208189e-02
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-#> 466        233     PHQ        Treatment Control - Treatment  4.799066e-02
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-#> 482        241     PHQ        Treatment Control - Treatment  3.789029e-02
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-#> 494        247     PHQ        Treatment Control - Treatment  6.579359e-02
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-#> 496        248     PHQ        Treatment Control - Treatment -2.938618e-01
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-#> 498        249     PHQ        Treatment Control - Treatment -3.524422e-02
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-#> 552        276     PHQ        Treatment Control - Treatment -1.933727e-01
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-#> 554        277     PHQ        Treatment Control - Treatment -1.653582e-01
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-#> 556        278     PHQ        Treatment Control - Treatment -8.845767e-02
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-#> 564        282     PHQ        Treatment Control - Treatment -5.428608e-02
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-#> 572        286     PHQ        Treatment Control - Treatment -4.969589e-02
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-#> 574        287     PHQ        Treatment Control - Treatment -1.844841e-01
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-#> 576        288     PHQ        Treatment Control - Treatment -1.878489e-01
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-#> 578        289     PHQ        Treatment Control - Treatment -4.273486e-01
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-#> 580        290     PHQ        Treatment Control - Treatment  6.649094e-02
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-#> 584        292     PHQ        Treatment Control - Treatment -6.712519e-02
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-#> 586        293     PHQ        Treatment Control - Treatment  2.596648e-02
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-#> 598        299     PHQ        Treatment Control - Treatment -6.980704e-02
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-#> 1532       766     PHQ        Treatment Control - Treatment  1.168415e-01
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-#> 1546       773     PHQ        Treatment Control - Treatment  3.868296e-04
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-#> 1554       777     PHQ        Treatment Control - Treatment -2.687211e-01
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-#> 1847       924     PHQ          Control Control - Treatment -9.191954e-02
-#> 1848       924     PHQ        Treatment Control - Treatment -9.191954e-02
-#> 1849       925     PHQ          Control Control - Treatment -1.569481e-01
-#> 1850       925     PHQ        Treatment Control - Treatment -1.569481e-01
-#> 1851       926     PHQ          Control Control - Treatment -9.422395e-02
-#> 1852       926     PHQ        Treatment Control - Treatment -9.422395e-02
-#> 1853       927     PHQ          Control Control - Treatment -2.836792e-02
-#> 1854       927     PHQ        Treatment Control - Treatment -2.836792e-02
-#> 1855       928     PHQ          Control Control - Treatment  0.000000e+00
-#> 1856       928     PHQ        Treatment Control - Treatment  0.000000e+00
-#> 1857       929     PHQ          Control Control - Treatment -5.639369e-02
-#> 1858       929     PHQ        Treatment Control - Treatment -5.639369e-02
-#> 1859       930     PHQ          Control Control - Treatment -3.976762e-02
-#> 1860       930     PHQ        Treatment Control - Treatment -3.976762e-02
-#> 1861       931     PHQ          Control Control - Treatment  1.966778e-03
-#> 1862       931     PHQ        Treatment Control - Treatment  1.966778e-03
-#> 1863       932     PHQ          Control Control - Treatment -2.026099e-01
-#> 1864       932     PHQ        Treatment Control - Treatment -2.026099e-01
-#> 1865       933     PHQ          Control Control - Treatment -8.875750e-02
-#> 1866       933     PHQ        Treatment Control - Treatment -8.875750e-02
-#> 1867       934     PHQ          Control Control - Treatment  0.000000e+00
-#> 1868       934     PHQ        Treatment Control - Treatment  0.000000e+00
-#> 1869       935     PHQ          Control Control - Treatment  0.000000e+00
-#> 1870       935     PHQ        Treatment Control - Treatment  0.000000e+00
-#> 1871       936     PHQ          Control Control - Treatment -3.555733e-01
-#> 1872       936     PHQ        Treatment Control - Treatment -3.555733e-01
-#> 1873       937     PHQ          Control Control - Treatment  0.000000e+00
-#> 1874       937     PHQ        Treatment Control - Treatment  0.000000e+00
-#> 1875       938     PHQ          Control Control - Treatment  1.742578e-01
-#> 1876       938     PHQ        Treatment Control - Treatment  1.742578e-01
-#> 1877       939     PHQ          Control Control - Treatment -2.739809e-01
-#> 1878       939     PHQ        Treatment Control - Treatment -2.739809e-01
-#> 1879       940     PHQ          Control Control - Treatment  2.062551e-01
-#> 1880       940     PHQ        Treatment Control - Treatment  2.062551e-01
-#> 1881       941     PHQ          Control Control - Treatment -5.617315e-02
-#> 1882       941     PHQ        Treatment Control - Treatment -5.617315e-02
-#> 1883       942     PHQ          Control Control - Treatment -5.760992e-02
-#> 1884       942     PHQ        Treatment Control - Treatment -5.760992e-02
-#> 1885       943     PHQ          Control Control - Treatment  1.129324e-02
-#> 1886       943     PHQ        Treatment Control - Treatment  1.129324e-02
-#> 1887       944     PHQ          Control Control - Treatment  2.892486e-02
-#> 1888       944     PHQ        Treatment Control - Treatment  2.892486e-02
-#> 1889       945     PHQ          Control Control - Treatment -1.174357e-01
-#> 1890       945     PHQ        Treatment Control - Treatment -1.174357e-01
-#> 1891       946     PHQ          Control Control - Treatment  9.137460e-02
-#> 1892       946     PHQ        Treatment Control - Treatment  9.137460e-02
-#> 1893       947     PHQ          Control Control - Treatment  1.089950e-01
-#> 1894       947     PHQ        Treatment Control - Treatment  1.089950e-01
-#> 1895       948     PHQ          Control Control - Treatment  4.075918e-02
-#> 1896       948     PHQ        Treatment Control - Treatment  4.075918e-02
-#> 1897       949     PHQ          Control Control - Treatment  2.542082e-02
-#> 1898       949     PHQ        Treatment Control - Treatment  2.542082e-02
-#> 1899       950     PHQ          Control Control - Treatment -1.533175e-01
-#> 1900       950     PHQ        Treatment Control - Treatment -1.533175e-01
-#> 1901       951     PHQ          Control Control - Treatment -3.898741e-01
-#> 1902       951     PHQ        Treatment Control - Treatment -3.898741e-01
-#> 1903       952     PHQ          Control Control - Treatment -2.985208e-01
-#> 1904       952     PHQ        Treatment Control - Treatment -2.985208e-01
-#> 1905       953     PHQ          Control Control - Treatment  5.807867e-02
-#> 1906       953     PHQ        Treatment Control - Treatment  5.807867e-02
-#> 1907       954     PHQ          Control Control - Treatment -9.676585e-03
-#> 1908       954     PHQ        Treatment Control - Treatment -9.676585e-03
-#> 1909       955     PHQ          Control Control - Treatment -1.190790e-01
-#> 1910       955     PHQ        Treatment Control - Treatment -1.190790e-01
-#> 1911       956     PHQ          Control Control - Treatment -1.257727e-01
-#> 1912       956     PHQ        Treatment Control - Treatment -1.257727e-01
-#> 1913       957     PHQ          Control Control - Treatment -4.846590e-02
-#> 1914       957     PHQ        Treatment Control - Treatment -4.846590e-02
-#> 1915       958     PHQ          Control Control - Treatment -1.733217e-01
-#> 1916       958     PHQ        Treatment Control - Treatment -1.733217e-01
-#> 1917       959     PHQ          Control Control - Treatment -1.457542e-01
-#> 1918       959     PHQ        Treatment Control - Treatment -1.457542e-01
-#> 1919       960     PHQ          Control Control - Treatment  1.406948e-01
-#> 1920       960     PHQ        Treatment Control - Treatment  1.406948e-01
-#> 1921       961     PHQ          Control Control - Treatment  1.252809e-01
-#> 1922       961     PHQ        Treatment Control - Treatment  1.252809e-01
-#> 1923       962     PHQ          Control Control - Treatment -4.883727e-02
-#> 1924       962     PHQ        Treatment Control - Treatment -4.883727e-02
-#> 1925       963     PHQ          Control Control - Treatment -3.010749e-01
-#> 1926       963     PHQ        Treatment Control - Treatment -3.010749e-01
-#> 1927       964     PHQ          Control Control - Treatment -6.140961e-02
-#> 1928       964     PHQ        Treatment Control - Treatment -6.140961e-02
-#> 1929       965     PHQ          Control Control - Treatment  0.000000e+00
-#> 1930       965     PHQ        Treatment Control - Treatment  0.000000e+00
-#> 1931       966     PHQ          Control Control - Treatment -9.755871e-03
-#> 1932       966     PHQ        Treatment Control - Treatment -9.755871e-03
-#> 1933       967     PHQ          Control Control - Treatment  3.020347e-01
-#> 1934       967     PHQ        Treatment Control - Treatment  3.020347e-01
-#> 1935       968     PHQ          Control Control - Treatment -1.159603e-01
-#> 1936       968     PHQ        Treatment Control - Treatment -1.159603e-01
-#> 1937       969     PHQ          Control Control - Treatment  0.000000e+00
-#> 1938       969     PHQ        Treatment Control - Treatment  0.000000e+00
-#> 1939       970     PHQ          Control Control - Treatment  0.000000e+00
-#> 1940       970     PHQ        Treatment Control - Treatment  0.000000e+00
-#> 1941       971     PHQ          Control Control - Treatment -1.211947e-01
-#> 1942       971     PHQ        Treatment Control - Treatment -1.211947e-01
-#> 1943       972     PHQ          Control Control - Treatment  9.438490e-02
-#> 1944       972     PHQ        Treatment Control - Treatment  9.438490e-02
-#> 1945       973     PHQ          Control Control - Treatment  0.000000e+00
-#> 1946       973     PHQ        Treatment Control - Treatment  0.000000e+00
-#> 1947       974     PHQ          Control Control - Treatment  7.675134e-02
-#> 1948       974     PHQ        Treatment Control - Treatment  7.675134e-02
-#> 1949       975     PHQ          Control Control - Treatment  0.000000e+00
-#> 1950       975     PHQ        Treatment Control - Treatment  0.000000e+00
-#> 1951       976     PHQ          Control Control - Treatment -8.027388e-02
-#> 1952       976     PHQ        Treatment Control - Treatment -8.027388e-02
-#> 1953       977     PHQ          Control Control - Treatment  5.687496e-02
-#> 1954       977     PHQ        Treatment Control - Treatment  5.687496e-02
-#> 1955       978     PHQ          Control Control - Treatment -1.216674e-01
-#> 1956       978     PHQ        Treatment Control - Treatment -1.216674e-01
-#> 1957       979     PHQ          Control Control - Treatment -5.007387e-02
-#> 1958       979     PHQ        Treatment Control - Treatment -5.007387e-02
-#> 1959       980     PHQ          Control Control - Treatment -3.475469e-02
-#> 1960       980     PHQ        Treatment Control - Treatment -3.475469e-02
-#> 1961       981     PHQ          Control Control - Treatment -7.349788e-02
-#> 1962       981     PHQ        Treatment Control - Treatment -7.349788e-02
-#> 1963       982     PHQ          Control Control - Treatment  1.295925e-01
-#> 1964       982     PHQ        Treatment Control - Treatment  1.295925e-01
-#> 1965       983     PHQ          Control Control - Treatment -5.067944e-02
-#> 1966       983     PHQ        Treatment Control - Treatment -5.067944e-02
-#> 1967       984     PHQ          Control Control - Treatment  0.000000e+00
-#> 1968       984     PHQ        Treatment Control - Treatment  0.000000e+00
-#> 1969       985     PHQ          Control Control - Treatment -1.618477e-01
-#> 1970       985     PHQ        Treatment Control - Treatment -1.618477e-01
-#> 1971       986     PHQ          Control Control - Treatment -3.402370e-01
-#> 1972       986     PHQ        Treatment Control - Treatment -3.402370e-01
-#> 1973       987     PHQ          Control Control - Treatment -1.353958e-01
-#> 1974       987     PHQ        Treatment Control - Treatment -1.353958e-01
-#> 1975       988     PHQ          Control Control - Treatment -2.834968e-02
-#> 1976       988     PHQ        Treatment Control - Treatment -2.834968e-02
-#> 1977       989     PHQ          Control Control - Treatment  2.783060e-02
-#> 1978       989     PHQ        Treatment Control - Treatment  2.783060e-02
-#> 1979       990     PHQ          Control Control - Treatment -1.096320e-01
-#> 1980       990     PHQ        Treatment Control - Treatment -1.096320e-01
-#> 1981       991     PHQ          Control Control - Treatment  0.000000e+00
-#> 1982       991     PHQ        Treatment Control - Treatment  0.000000e+00
-#> 1983       992     PHQ          Control Control - Treatment -1.494135e-01
-#> 1984       992     PHQ        Treatment Control - Treatment -1.494135e-01
-#> 1985       993     PHQ          Control Control - Treatment -2.259981e-02
-#> 1986       993     PHQ        Treatment Control - Treatment -2.259981e-02
-#> 1987       994     PHQ          Control Control - Treatment -5.661833e-02
-#> 1988       994     PHQ        Treatment Control - Treatment -5.661833e-02
-#> 1989       995     PHQ          Control Control - Treatment  0.000000e+00
-#> 1990       995     PHQ        Treatment Control - Treatment  0.000000e+00
-#> 1991       996     PHQ          Control Control - Treatment  0.000000e+00
-#> 1992       996     PHQ        Treatment Control - Treatment  0.000000e+00
-#> 1993       997     PHQ          Control Control - Treatment  0.000000e+00
-#> 1994       997     PHQ        Treatment Control - Treatment  0.000000e+00
-#> 1995       998     PHQ          Control Control - Treatment  1.711551e-01
-#> 1996       998     PHQ        Treatment Control - Treatment  1.711551e-01
-#> 1997       999     PHQ          Control Control - Treatment -4.478137e-02
-#> 1998       999     PHQ        Treatment Control - Treatment -4.478137e-02
-#> 1999      1000     PHQ          Control Control - Treatment -1.195082e-01
-#> 2000      1000     PHQ        Treatment Control - Treatment -1.195082e-01

+
+bootstrap(model, exper, c(direct_effect = direct_effect))$direct_effect |>
+    head(10)

+
#>    bootstrap outcome indirect_setting            contrast direct_effect
+#> 1          1     PHQ          Control Control - Treatment   -0.07762666
+#> 2          1     PHQ        Treatment Control - Treatment   -0.07762666
+#> 3          2     PHQ          Control Control - Treatment   -0.13247632
+#> 4          2     PHQ        Treatment Control - Treatment   -0.13247632
+#> 5          3     PHQ          Control Control - Treatment   -0.08455178
+#> 6          3     PHQ        Treatment Control - Treatment   -0.08455178
+#> 7          4     PHQ          Control Control - Treatment   -0.10422923
+#> 8          4     PHQ        Treatment Control - Treatment   -0.10422923
+#> 9          5     PHQ          Control Control - Treatment   -0.15210409
+#> 10         5     PHQ        Treatment Control - Treatment   -0.15210409

 
We can also generate synthetic nulls to calibrate selection sets. The
 third argument says which set of edges we want to remove under the null.
 In this case we will generate synthetic null data where there is known
@@ -2343,7 +414,7 @@ 
Inference
+
 contrast <- null_contrast(model, exper, "M->Y", indirect_pathwise)
 fdr <- fdr_summary(contrast, "indirect_pathwise", 0.05)
 fdr

@@ -2360,14 +431,78 @@ 
Inference#>  8 synthetic PHQ     ASV1             0       drop_last     8   0.375 FALSE
 #>  9 synthetic PHQ     ASV2             0       drop_last     9   0.444 FALSE
 #> 10 synthetic PHQ     ASV5             0       drop_last    10   0.5   FALSE

+
+
#> R version 4.4.1 (2024-06-14)
+#> Platform: aarch64-apple-darwin20
+#> Running under: macOS Sonoma 14.5
+#> 
+#> Matrix products: default
+#> BLAS:   /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/lib/libRblas.0.dylib 
+#> LAPACK: /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/lib/libRlapack.dylib;  LAPACK version 3.12.0
+#> 
+#> locale:
+#> [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
+#> 
+#> time zone: America/Chicago
+#> tzcode source: internal
+#> 
+#> attached base packages:
+#> [1] stats4    stats     graphics  grDevices utils     datasets  methods  
+#> [8] base     
+#> 
+#> other attached packages:
+#>  [1] ggraph_2.2.1                multimedia_0.1.0           
+#>  [3] tidyselect_1.2.1            SummarizedExperiment_1.35.1
+#>  [5] Biobase_2.65.0              GenomicRanges_1.57.1       
+#>  [7] GenomeInfoDb_1.41.1         IRanges_2.39.2             
+#>  [9] S4Vectors_0.43.2            BiocGenerics_0.51.0        
+#> [11] MatrixGenerics_1.17.0       matrixStats_1.3.0          
+#> [13] ggplot2_3.5.1               BiocStyle_2.33.1           
+#> 
+#> loaded via a namespace (and not attached):
+#>   [1] gridExtra_2.3           permute_0.9-7           rlang_1.1.4            
+#>   [4] magrittr_2.0.3          ade4_1.7-22             compiler_4.4.1         
+#>   [7] mgcv_1.9-1              systemfonts_1.1.0       vctrs_0.6.5            
+#>  [10] reshape2_1.4.4          stringr_1.5.1           shape_1.4.6.1          
+#>  [13] pkgconfig_2.0.3         crayon_1.5.3            fastmap_1.2.0          
+#>  [16] XVector_0.45.0          labeling_0.4.3          utf8_1.2.4             
+#>  [19] rmarkdown_2.28          UCSC.utils_1.1.0        glmnetUtils_1.1.9      
+#>  [22] ragg_1.3.2              purrr_1.0.2             glmnet_4.1-8           
+#>  [25] xfun_0.47               zlibbioc_1.51.1         cachem_1.1.0           
+#>  [28] jsonlite_1.8.8          biomformat_1.33.0       progress_1.2.3         
+#>  [31] highr_0.11              rhdf5filters_1.17.0     DelayedArray_0.31.11   
+#>  [34] tweenr_2.0.3            Rhdf5lib_1.27.0         parallel_4.4.1         
+#>  [37] prettyunits_1.2.0       cluster_2.1.6           R6_2.5.1               
+#>  [40] bslib_0.8.0             stringi_1.8.4           jquerylib_0.1.4        
+#>  [43] Rcpp_1.0.13             bookdown_0.40           iterators_1.0.14       
+#>  [46] knitr_1.48              Matrix_1.7-0            splines_4.4.1          
+#>  [49] igraph_2.0.3            viridis_0.6.5           abind_1.4-5            
+#>  [52] yaml_2.3.10             vegan_2.6-8             codetools_0.2-20       
+#>  [55] lattice_0.22-6          tibble_3.2.1            plyr_1.8.9             
+#>  [58] withr_3.0.1             evaluate_0.24.0         desc_1.4.3             
+#>  [61] survival_3.7-0          polyclip_1.10-7         Biostrings_2.73.1      
+#>  [64] pillar_1.9.0            BiocManager_1.30.24     phyloseq_1.49.0        
+#>  [67] foreach_1.5.2           insight_0.20.3          generics_0.1.3         
+#>  [70] hms_1.1.3               munsell_0.5.1           scales_1.3.0           
+#>  [73] glue_1.7.0              tools_4.4.1             data.table_1.16.0      
+#>  [76] graphlayouts_1.1.1      fs_1.6.4                tidygraph_1.3.1        
+#>  [79] rhdf5_2.49.0            grid_4.4.1              tidyr_1.3.1            
+#>  [82] ape_5.8                 colorspace_2.1-1        nlme_3.1-166           
+#>  [85] formula.tools_1.7.1     GenomeInfoDbData_1.2.12 ggforce_0.4.2          
+#>  [88] cli_3.6.3               textshaping_0.4.0       fansi_1.0.6            
+#>  [91] viridisLite_0.4.2       S4Arrays_1.5.7          dplyr_1.1.4            
+#>  [94] gtable_0.3.5            sass_0.4.9              digest_0.6.37          
+#>  [97] operator.tools_1.6.3    ggrepel_0.9.5           SparseArray_1.5.31     
+#> [100] farver_2.1.2            htmlwidgets_1.6.4       memoise_2.0.1          
+#> [103] htmltools_0.5.8.1       pkgdown_2.1.0           multtest_2.61.0        
+#> [106] lifecycle_1.0.4         httr_1.4.7              MASS_7.3-61

 

   

 
   
+      

 
 

 
@@ -2375,21 +510,21 @@ 
Inference
   

-
Developed by Kris Sankaran.

+
Developed by Kris Sankaran, Hanying Jiang.

 

 
 

   

-
Site built with pkgdown 2.0.9.

+
Site built with pkgdown 2.1.0.

 

 
       
 

 
-  
 
 
-  
+
+
 
   
 
diff --git a/docs/news/index.html b/docs/news/index.html
new file mode 100644
index 0000000..4e2b89b
--- /dev/null
+++ b/docs/news/index.html
@@ -0,0 +1,98 @@
+
+Changelog • multimedia
+
+
+    

+      

+
+
+
+      

+  

+    

+      
Changelog 

+      Source: NEWS.md
+    

+
+    

+
multimedia 0.1.0

+
  • Initial CRAN submission.
    • 
+

+  

+
+  
+
+

+
+
+      

+  
Developed by Kris Sankaran, Hanying Jiang.

+

+
+

+  
Site built with pkgdown 2.1.0.

+

+
+      

+
+
+
+
+
+
+  
+
diff --git a/docs/pkgdown.yml b/docs/pkgdown.yml
index 278743e..066a6a2 100644
--- a/docs/pkgdown.yml
+++ b/docs/pkgdown.yml
@@ -6,4 +6,4 @@ articles:
   illustration: illustration.html
   mindfulness: mindfulness.html
   random: random.html
-last_built: 2024-08-28T00:17Z
+last_built: 2024-08-28T22:54Z
diff --git a/docs/reference/bind_mediation.html b/docs/reference/bind_mediation.html
index ca7dbc5..1186d85 100644
--- a/docs/reference/bind_mediation.html
+++ b/docs/reference/bind_mediation.html
@@ -97,7 +97,7 @@ 
Value

     

     
Examples

     
exper <- demo_joy() |>
-  mediation_data("PHQ", "treatment", starts_with("ASV"))
+    mediation_data("PHQ", "treatment", starts_with("ASV"))
 exper
 #> [Mediation Data] 
 #> 100 samples with measurements for, 
@@ -309,7 +309,7 @@ 
Examples

 #> 100   Control
 
 exper <- demo_spline(tau = c(2, 1)) |>
-  mediation_data(starts_with("outcome"), "treatment", "mediator")
+    mediation_data(starts_with("outcome"), "treatment", "mediator")
 exper
 #> [Mediation Data] 
 #> 5000 samples with measurements for, 
diff --git a/docs/reference/bootstrap.html b/docs/reference/bootstrap.html
index f5c2dcb..850d8b8 100644
--- a/docs/reference/bootstrap.html
+++ b/docs/reference/bootstrap.html
@@ -115,9 +115,9 @@ 
Value

     
Examples

     
# example with null data
 exper <- demo_joy() |>
-  mediation_data("PHQ", "treatment", starts_with("ASV"))
+    mediation_data("PHQ", "treatment", starts_with("ASV"))
 multimedia(exper) |>
-  bootstrap(exper, B = 100)
+    bootstrap(exper, B = 100)
 #> Bootstrapping direct_effect
 #> $direct_effect
 #>     bootstrap outcome indirect_setting            contrast direct_effect
@@ -325,13 +325,16 @@ 
Examples

 
 # example with another dataset
 exper <- demo_spline(n_samples = 100, tau = c(2, 1)) |>
-  mediation_data(starts_with("outcome"), "treatment", "mediator")
+    mediation_data(starts_with("outcome"), "treatment", "mediator")
 samples <- multimedia(exper, rf_model(num.trees = 1e3)) |>
-  bootstrap(exper, B = 100)
+    bootstrap(exper, B = 100)
 #> Bootstrapping direct_effect
 ggplot2::ggplot(samples$direct_effect) +
-  ggplot2::geom_histogram(ggplot2::aes(direct_effect, fill = indirect_setting), bins = 15) +
-  ggplot2::facet_wrap(~outcome, scales = "free")
+    ggplot2::geom_histogram(
+        ggplot2::aes(direct_effect, fill = indirect_setting),
+        bins = 15
+    ) +
+    ggplot2::facet_wrap(~outcome, scales = "free")
 
 

     

diff --git a/docs/reference/brms_model.html b/docs/reference/brms_model.html
index 79eb2a3..7332e50 100644
--- a/docs/reference/brms_model.html
+++ b/docs/reference/brms_model.html
@@ -1,6 +1,7 @@
 
-Bayesian Regression Model across Responses — brms_model • multimediaBayesian Regression Model across Responses — brms_model • multimedia
@@ -69,8 +70,9 @@ 
Bayesian Regression Model across Responses

     

 
     

-    
Apply a Bayesian regression model in parallel across each response $y$ in
-an outcome or mediation model. This can be helpful when we want to share information across related

+    
Apply a Bayesian regression model in parallel across each response $y$ in an
+outcome or mediation model. This can be helpful when we want to share
+information across related

     

 
     

@@ -98,9 +100,9 @@ 
See also

     

     
Examples

     
exper <- demo_joy() |>
-  mediation_data("PHQ", "treatment", starts_with("ASV"))
+    mediation_data("PHQ", "treatment", starts_with("ASV"))
 multimedia(exper, brms_model()) |>
-  estimate(exper)
+    estimate(exper)
 #> Compiling Stan program...
 #> Start sampling
 #> [Multimedia Analysis] 
@@ -114,9 +116,9 @@ 
Examples

 
 # example with another dataset
 exper <- demo_spline(tau = c(2, 1)) |>
-  mediation_data(starts_with("outcome"), "treatment", "mediator")
+    mediation_data(starts_with("outcome"), "treatment", "mediator")
 fit <- multimedia(exper, brms_model()) |>
-  estimate(exper)
+    estimate(exper)
 #> Compiling Stan program...
 #> Start sampling
 #> Start sampling
diff --git a/docs/reference/contrast_predictions.html b/docs/reference/contrast_predictions.html
index 7bd7ab0..2ae88b0 100644
--- a/docs/reference/contrast_predictions.html
+++ b/docs/reference/contrast_predictions.html
@@ -111,9 +111,9 @@ 
Value

     

     
Examples

     
exper <- demo_joy() |>
-  mediation_data("PHQ", "treatment", starts_with("ASV"))
+    mediation_data("PHQ", "treatment", starts_with("ASV"))
 model <- multimedia(exper) |>
-  estimate(exper)
+    estimate(exper)
 t1 <- data.frame(treatment = factor("Treatment"))
 t2 <- data.frame(treatment = factor("Control"))
 profile1 <- setup_profile(model, t1, t1)
diff --git a/docs/reference/contrast_samples.html b/docs/reference/contrast_samples.html
index d77e625..23cae6f 100644
--- a/docs/reference/contrast_samples.html
+++ b/docs/reference/contrast_samples.html
@@ -113,9 +113,9 @@ 
Value

     

     
Examples

     
exper <- demo_joy() |>
-  mediation_data("PHQ", "treatment", starts_with("ASV"))
+    mediation_data("PHQ", "treatment", starts_with("ASV"))
 model <- multimedia(exper) |>
-  estimate(exper)
+    estimate(exper)
 t1 <- data.frame(treatment = factor("Treatment"))
 t2 <- data.frame(treatment = factor("Control"))
 profile1 <- setup_profile(model, t1, t1)
@@ -130,10 +130,13 @@ 
Examples

 #> 1 -0.2344377
 #> 
 
-samples <- purrr::map(seq_len(100), ~ contrast_samples(model, profile1, profile2))
-hist(sapply(samples, \(x) x[[1]]$ASV1) )
+samples <- purrr::map(
+    seq_len(100),
+    ~ contrast_samples(model, profile1, profile2)
+)
+hist(sapply(samples, \(x) x[[1]]$ASV1))
 
-hist(sapply(samples, \(x) x[[1]]$ASV2) )
+hist(sapply(samples, \(x) x[[1]]$ASV2))
 
 

     

diff --git a/docs/reference/direct_effect.html b/docs/reference/direct_effect.html
index c5a43d5..a4dbacd 100644
--- a/docs/reference/direct_effect.html
+++ b/docs/reference/direct_effect.html
@@ -1,6 +1,9 @@
 
 Direct Effects from Estimated Model — direct_effect • multimedia
@@ -70,7 +73,10 @@ 
Direct Effects from Estimated Model

 
     

     
Estimate direct effects associated with a multimedia model. These estimates
-are formed using Equation (10) of our preprint:

+are formed using Equation (10) of our paper. Rather than providing this
+average, this function returns the estimated difference for each $j$. To
+average across all j, this result can be passed to the ' effect_summary
+function.

     

 
     

@@ -106,15 +112,6 @@ 
Arguments

     
Value

     
A data.frame summarizing the direct effects associated with different
 settings of j in the equation above.

-    

-    

-    
Details

-    
$$
-\frac{1}{2} \sum_{j = 0}^{1} \sum_{i = 1}^{N} \hat{Y}_{i}(t2, \hat{M}(t2)) - \hat{Y}_{i}(t1, \hat{M}(t1))
-$$

-
Rather than providing this average, this function returns the estimated
-difference for each $j$. To average across all j, this result can be passed
-to the ' effect_summary function.

     

     

     
See also

@@ -125,9 +122,9 @@ 
See also

     
Examples

     
# example with null data
 exper <- demo_joy() |>
-  mediation_data("PHQ", "treatment", starts_with("ASV"))
+    mediation_data("PHQ", "treatment", starts_with("ASV"))
 fit <- multimedia(exper) |>
-  estimate(exper)
+    estimate(exper)
 
 direct_effect(fit)
 #>   outcome indirect_setting            contrast direct_effect
@@ -144,9 +141,9 @@ 
Examples

 
 # example with another dataset
 exper <- demo_spline(tau = c(2, 1)) |>
-  mediation_data(starts_with("outcome"), "treatment", "mediator")
+    mediation_data(starts_with("outcome"), "treatment", "mediator")
 fit <- multimedia(exper) |>
-  estimate(exper)
+    estimate(exper)
 direct_effect(fit)
 #>     outcome indirect_setting contrast direct_effect
 #> 1 outcome_1                0    0 - 1     -1.978844
diff --git a/docs/reference/edges-multimedia-method.html b/docs/reference/edges-multimedia-method.html
index 4650665..a7d5af3 100644
--- a/docs/reference/edges-multimedia-method.html
+++ b/docs/reference/edges-multimedia-method.html
@@ -96,9 +96,9 @@ 
Value

     

     
Examples

     
exper <- demo_joy() |>
-  mediation_data("PHQ", "treatment", starts_with("ASV"))
+    mediation_data("PHQ", "treatment", starts_with("ASV"))
 multimedia(exper) |>
-  edges()
+    edges()
 #> # A tbl_graph: 8 nodes and 17 edges
 #> #
 #> # A directed acyclic simple graph with 1 component
diff --git a/docs/reference/effect_summary.html b/docs/reference/effect_summary.html
index d3df2b8..1c5e747 100644
--- a/docs/reference/effect_summary.html
+++ b/docs/reference/effect_summary.html
@@ -101,11 +101,11 @@ 
See also

     
Examples

     
# example with null data
 exper <- demo_joy() |>
-  mediation_data("PHQ", "treatment", starts_with("ASV"))
+    mediation_data("PHQ", "treatment", starts_with("ASV"))
 multimedia(exper) |>
-  estimate(exper) |>
-  direct_effect() |>
-  effect_summary()
+    estimate(exper) |>
+    direct_effect() |>
+    effect_summary()
 #> # A tibble: 1 × 2
 #>   outcome direct_effect
 #>   <chr>           <dbl>
@@ -113,11 +113,11 @@ 
Examples

 
 # example with another dataset
 exper <- demo_spline(tau = c(2, 1)) |>
-  mediation_data(starts_with("outcome"), "treatment", "mediator")
+    mediation_data(starts_with("outcome"), "treatment", "mediator")
 multimedia(exper) |>
-  estimate(exper) |>
-  direct_effect() |>
-  effect_summary()
+    estimate(exper) |>
+    direct_effect() |>
+    effect_summary()
 #> # A tibble: 2 × 2
 #>   outcome   direct_effect
 #>   <chr>             <dbl>
diff --git a/docs/reference/estimate.html b/docs/reference/estimate.html
index 5c6a7ff..0b90db9 100644
--- a/docs/reference/estimate.html
+++ b/docs/reference/estimate.html
@@ -105,9 +105,9 @@ 
Value

     

     
Examples

     
exper <- demo_joy() |>
-  mediation_data("PHQ", "treatment", starts_with("ASV"))
+    mediation_data("PHQ", "treatment", starts_with("ASV"))
 multimedia(exper) |>
-  estimate(exper)
+    estimate(exper)
 #> [Multimedia Analysis] 
 #> Treatments: treatment 
 #> Outcomes: PHQ 
@@ -119,9 +119,9 @@ 
Examples

 
 # example with another dataset
 exper <- demo_spline(tau = c(2, 1)) |>
-  mediation_data(starts_with("outcome"), "treatment", "mediator")
+    mediation_data(starts_with("outcome"), "treatment", "mediator")
 multimedia(exper) |>
-  estimate(exper)
+    estimate(exper)
 #> [Multimedia Analysis] 
 #> Treatments: treatment 
 #> Outcomes: outcome_1, outcome_2 
@@ -133,9 +133,9 @@ 
Examples

 
 # example with another model
 exper <- demo_spline(tau = c(2, 1)) |>
-  mediation_data(starts_with("outcome"), "treatment", "mediator")
+    mediation_data(starts_with("outcome"), "treatment", "mediator")
 multimedia(exper, rf_model()) |>
-  estimate(exper)
+    estimate(exper)
 #> [Multimedia Analysis] 
 #> Treatments: treatment 
 #> Outcomes: outcome_1, outcome_2 
diff --git a/docs/reference/exper_df.html b/docs/reference/exper_df.html
index 17f457c..f00cda4 100644
--- a/docs/reference/exper_df.html
+++ b/docs/reference/exper_df.html
@@ -97,7 +97,7 @@ 
Value

     

     
Examples

     
demo_joy() |>
-  multimedia:::exper_df()
+    multimedia:::exper_df()
 #>             ASV1        ASV2         ASV3        ASV4        ASV5 treatment
 #> 1   -0.782300340 -0.70354655 -3.085106383 -1.44937373 -1.52974524   Control
 #> 2    0.346099273 -0.42673424 -0.510881446 -0.09827899  0.72633032 Treatment
diff --git a/docs/reference/fdr_summary.html b/docs/reference/fdr_summary.html
index 2f37d1d..1362382 100644
--- a/docs/reference/fdr_summary.html
+++ b/docs/reference/fdr_summary.html
@@ -88,9 +88,9 @@ 
Arguments

 
 
 
contrast

-
A data.frame summarizing the differences between outcomes across
-hypothetical treatments, typically as output by null_contrast. Each row
-is one outcome in one hypothetical scenario.

+
A data.frame summarizing the differences between outcomes
+across hypothetical treatments, typically as output by null_contrast.
+Each row is one outcome in one hypothetical scenario.

 
 
 
effect

@@ -114,11 +114,11 @@ 
Value

     
Examples

     
# example with null data - notice synthetic data has larger effect.
 exper <- demo_joy() |>
-  mediation_data("PHQ", "treatment", starts_with("ASV"))
+    mediation_data("PHQ", "treatment", starts_with("ASV"))
 multimedia(exper) |>
-  estimate(exper) |>
-  null_contrast(exper) |>
-  fdr_summary("direct_effect")
+    estimate(exper) |>
+    null_contrast(exper) |>
+    fdr_summary("direct_effect")
 #> Fitting the nullified model...
 #> Generating synthetic data...
 #> Fitting the full model on synthetic data...
@@ -134,9 +134,9 @@ 
Examples

 #> 2 real      PHQ           -0.0594     2     0.5 FALSE
 
 multimedia(exper) |>
-  estimate(exper) |>
-  null_contrast(exper, "M->Y", indirect_overall) |>
-  fdr_summary("indirect_overall")
+    estimate(exper) |>
+    null_contrast(exper, "M->Y", indirect_overall) |>
+    fdr_summary("indirect_overall")
 #> Fitting the nullified model...
 #> Generating synthetic data...
 #> Fitting the full model on synthetic data...
@@ -149,11 +149,11 @@ 
Examples

 
 # example with another dataset - synthetic effect is smaller.
 exper <- demo_spline(tau = c(2, 1)) |>
-  mediation_data(starts_with("outcome"), "treatment", "mediator")
+    mediation_data(starts_with("outcome"), "treatment", "mediator")
 multimedia(exper) |>
-  estimate(exper) |>
-  null_contrast(exper) |>
-  fdr_summary("direct_effect")
+    estimate(exper) |>
+    null_contrast(exper) |>
+    fdr_summary("direct_effect")
 #> Fitting the nullified model...
 #> Generating synthetic data...
 #> Fitting the full model on synthetic data...
@@ -167,9 +167,9 @@ 
Examples

 #> 4 synthetic outcome_2        0.0281     4   0.5   FALSE
 
 multimedia(exper) |>
-  estimate(exper) |>
-  null_contrast(exper, "M->Y", indirect_overall) |>
-  fdr_summary("indirect_overall")
+    estimate(exper) |>
+    null_contrast(exper, "M->Y", indirect_overall) |>
+    fdr_summary("indirect_overall")
 #> Fitting the nullified model...
 #> Generating synthetic data...
 #> Fitting the full model on synthetic data...
diff --git a/docs/reference/glmnet_model.html b/docs/reference/glmnet_model.html
index dc932e8..919e2bf 100644
--- a/docs/reference/glmnet_model.html
+++ b/docs/reference/glmnet_model.html
@@ -102,9 +102,9 @@ 
See also

     

     
Examples

     
exper <- demo_joy() |>
-  mediation_data("PHQ", "treatment", starts_with("ASV"))
+    mediation_data("PHQ", "treatment", starts_with("ASV"))
 multimedia(exper, glmnet_model(lambda = 1)) |>
-  estimate(exper)
+    estimate(exper)
 #> [Multimedia Analysis] 
 #> Treatments: treatment 
 #> Outcomes: PHQ 
@@ -115,7 +115,7 @@ 
Examples

 #> outcome: A fitted glmnet_model(). 
 
 multimedia(exper, glmnet_model(lambda = 1), glmnet_model()) |>
-  estimate(exper)
+    estimate(exper)
 #> [Multimedia Analysis] 
 #> Treatments: treatment 
 #> Outcomes: PHQ 
@@ -127,9 +127,9 @@ 
Examples

 
 # example with another dataset
 exper <- demo_spline(tau = c(2, 1)) |>
-  mediation_data(starts_with("outcome"), "treatment", "mediator")
+    mediation_data(starts_with("outcome"), "treatment", "mediator")
 multimedia(exper, glmnet_model(lambda = 0.1)) |>
-  estimate(exper)
+    estimate(exper)
 #> [Multimedia Analysis] 
 #> Treatments: treatment 
 #> Outcomes: outcome_1, outcome_2 
diff --git a/docs/reference/indirect_overall.html b/docs/reference/indirect_overall.html
index aeb75d9..bca517f 100644
--- a/docs/reference/indirect_overall.html
+++ b/docs/reference/indirect_overall.html
@@ -108,19 +108,16 @@ 
Value

     

     
Details

     
Estimate direct effects associated with a multimedia model. These estimates
-are formed using Equation (10) of our preprint:

-
$$
-\frac{1}{2} \sum_{j = 0}^{1} \sum_{i = 1}^{N} \hat{Y}_{i}(t2, \hat{M}(t2)) - \hat{Y}_{i}(t1, \hat{M}(t1))
-$$

+are formed using Equation (10) of our preprint.

     

 
     

     
Examples

     
# example with null data
 exper <- demo_joy() |>
-  mediation_data("PHQ", "treatment", starts_with("ASV"))
+    mediation_data("PHQ", "treatment", starts_with("ASV"))
 fit <- multimedia(exper) |>
-  estimate(exper)
+    estimate(exper)
 
 indirect_overall(fit)
 #>   outcome direct_setting            contrast indirect_effect
@@ -129,9 +126,9 @@ 
Examples

 
 # example with another dataset
 exper <- demo_spline(tau = c(2, 1)) |>
-  mediation_data(starts_with("outcome"), "treatment", "mediator")
+    mediation_data(starts_with("outcome"), "treatment", "mediator")
 fit <- multimedia(exper) |>
-  estimate(exper)
+    estimate(exper)
 indirect_overall(fit)
 #>     outcome direct_setting contrast indirect_effect
 #> 1 outcome_1              0    0 - 1      -0.5951599
diff --git a/docs/reference/indirect_pathwise.html b/docs/reference/indirect_pathwise.html
index ca4d4e5..da2a489 100644
--- a/docs/reference/indirect_pathwise.html
+++ b/docs/reference/indirect_pathwise.html
@@ -110,9 +110,9 @@ 
Value

     
Examples

     
# example with null data
 exper <- demo_joy() |>
-  mediation_data("PHQ", "treatment", starts_with("ASV"))
+    mediation_data("PHQ", "treatment", starts_with("ASV"))
 fit <- multimedia(exper) |>
-  estimate(exper)
+    estimate(exper)
 indirect_pathwise(fit)
 #> Indirect effects for direct setting 1
 #> Indirect effects for direct setting 2
@@ -130,9 +130,9 @@ 
Examples

 
 # example with another dataset
 exper <- demo_spline(tau = c(2, 1)) |>
-  mediation_data(starts_with("outcome"), "treatment", "mediator")
+    mediation_data(starts_with("outcome"), "treatment", "mediator")
 fit <- multimedia(exper) |>
-  estimate(exper)
+    estimate(exper)
 indirect_pathwise(fit)
 #> Indirect effects for direct setting 1
 #> Indirect effects for direct setting 2
diff --git a/docs/reference/lnm_model.html b/docs/reference/lnm_model.html
index 8f761cf..0eb3902 100644
--- a/docs/reference/lnm_model.html
+++ b/docs/reference/lnm_model.html
@@ -110,8 +110,8 @@ 
Examples

 #>   This procedure has not been thoroughly tested and may be unstable 
 #>   or buggy. The interface is subject to change. 
 #> ------------------------------------------------------------ 
-#> Gradient evaluation took 3.7e-05 seconds 
-#> 1000 transitions using 10 leapfrog steps per transition would take 0.37 seconds. 
+#> Gradient evaluation took 6.1e-05 seconds 
+#> 1000 transitions using 10 leapfrog steps per transition would take 0.61 seconds. 
 #> Adjust your expectations accordingly! 
 #> Begin eta adaptation. 
 #> Iteration:   1 / 250 [  0%]  (Adaptation) 
diff --git a/docs/reference/mediation_data.html b/docs/reference/mediation_data.html
index 7ffbd08..432dc84 100644
--- a/docs/reference/mediation_data.html
+++ b/docs/reference/mediation_data.html
@@ -129,7 +129,9 @@ 
See also

     

     
Examples

     
# multiple outcomes, one mediator
-mediation_data(demo_spline(), starts_with("outcome"), "treatment", "mediator")
+mediation_data(
+    demo_spline(), starts_with("outcome"), "treatment", "mediator"
+)
 #> [Mediation Data] 
 #> 5000 samples with measurements for, 
 #> 1 treatment: treatment 
diff --git a/docs/reference/mediation_models.html b/docs/reference/mediation_models.html
index af63839..79775e3 100644
--- a/docs/reference/mediation_models.html
+++ b/docs/reference/mediation_models.html
@@ -91,19 +91,18 @@ 
Value

 
     

     
Examples

-    
exper <- mediation_data(
-  mindfulness, 
-  phyloseq::taxa_names(mindfulness), 
-  "treatment", 
-  starts_with("mediator"),   
-  "subject"
+    
data(mindfulness)
+exper <- mediation_data(
+    mindfulness,
+    phyloseq::taxa_names(mindfulness),
+    "treatment",
+    starts_with("mediator"),
+    "subject"
 )
-#> Error in eval(expr, envir, enclos): object 'mindfulness' not found
 
 m <- multimedia(exper)
-#> Error in eval(expr, envir, enclos): object 'exper' not found
 mediation_models(m)
-#> Error in eval(expr, envir, enclos): object 'm' not found
+#> Error in mediation_models(m): no slot of name "mediaton" for this object of class "multimedia"
 

     

   

diff --git a/docs/reference/mediators-mediation_data-method.html b/docs/reference/mediators-mediation_data-method.html
index aaa2853..d6c560f 100644
--- a/docs/reference/mediators-mediation_data-method.html
+++ b/docs/reference/mediators-mediation_data-method.html
@@ -86,13 +86,14 @@ 
Arguments

 

     

     
Value

-    
m A data.frame whose rows are samples and columns are values of mediators across those samples.

+    
m A data.frame whose rows are samples and columns are values of
+mediators across those samples.

     

 
     

     
Examples

     
exper <- demo_joy() |>
-  mediation_data("PHQ", "treatment", starts_with("ASV"))
+    mediation_data("PHQ", "treatment", starts_with("ASV"))
 mediators(exper)
 #>            ASV1          ASV2         ASV3         ASV4        ASV5
 #> 1    0.73853614  0.0627456951 -0.668084328  0.559650807  2.35437797
diff --git a/docs/reference/mediators-multimedia-method.html b/docs/reference/mediators-multimedia-method.html
index ae952a2..d6f900f 100644
--- a/docs/reference/mediators-multimedia-method.html
+++ b/docs/reference/mediators-multimedia-method.html
@@ -98,9 +98,9 @@ 
Value

     

     
Examples

     
exper <- demo_joy() |>
-  mediation_data("PHQ", "treatment", starts_with("ASV"))
+    mediation_data("PHQ", "treatment", starts_with("ASV"))
 multimedia(exper) |>
-  mediators()
+    mediators()
 #> [1] "ASV1" "ASV2" "ASV3" "ASV4" "ASV5"
 

     

diff --git a/docs/reference/mediators-set-mediation_data-method.html b/docs/reference/mediators-set-mediation_data-method.html
index ee782a3..a6e8b53 100644
--- a/docs/reference/mediators-set-mediation_data-method.html
+++ b/docs/reference/mediators-set-mediation_data-method.html
@@ -98,7 +98,7 @@ 
Value

     

     
Examples

     
exper <- demo_joy() |>
-  mediation_data("PHQ", "treatment", starts_with("ASV"))
+    mediation_data("PHQ", "treatment", starts_with("ASV"))
 mediators(exper) <- data.frame(m = 1:10)
 exper
 #> [Mediation Data] 
diff --git a/docs/reference/mindfulness.html b/docs/reference/mindfulness.html
index f14d494..b5c8830 100644
--- a/docs/reference/mindfulness.html
+++ b/docs/reference/mindfulness.html
@@ -89,6 +89,11 @@ 
Value

 associated phylogenetic tree.

     

 
+    

+    
Examples

+    
data(mindfulness)
+

+