sibregresr

The goal of sibregresr is to predict salmon returns using sibling regression. The regressions are conducted within a dynamic linear modeling framework and model averaging is used.

Installation

You can install the development version of sibregresr from GitHub with:

# install.packages("devtools")
devtools::install_github("wdfw-fp/sibregresr")

Example

This is a basic example which shows you how to solve a common problem:

library(sibregresr)
## basic example code

## to come...

Methods description

The first step in forecasting the returns of a given stock $y_{a,t}$ of age $a$ in year $t$ is to fit eight different models to observed returns through year $t-1$. The eight different models are variations of a sibling regression model fit on the log scale with time-varying intercept and slope:

where $\alpha_t$ and $\beta_t$ are an intercept and a slope for the log-transformed returns of the previous age in the previous year, respectively, and both are allowed to vary across years as random walks with process error variances $w_{\alpha, t}$ and $w_{\beta, t}$ respectively. The residual $v_t$ is assumed to be normally distributed around zero with variance $V_t$. Together with a vague prior distribution for the values of $\alpha_0$ and $\beta_0$ (the slope and intercept prior to the first year) these equations define the “full” sibling regression models.

The seven other models are simplified versions of this full model where:

1. the slope is assumed to constant through time (i.e., $w_{\beta, t}=0$);
2. the intercept is assumed to be constant through time;
3. the slope and intercept are assumed to be constant through time;
4. the intercept is assumed to be zero (i.e., $\alpha_t=0$);
5. the intercept is assumed to be zero and the slope is assumed to be constant through time;
6. the slope is assumed to be zero; and
7. the slope is assumed to be zero and the intercept is assumed to be constant through time.

Together with the full model, this list comprises the eight models considered in forecasting. The models are fit using the dlm package (Petris 2010) in the R statistical computing environment.

Once the eight models have been fit, each is used to make a prediction of returns in the upcoming year and an ensemble forecast is generated by taking a weighted average of the predictions. By default, the ensemble model weights are calculated for each model $m$ in the set ($\mathcal{M}$) of 8 models based on their AICc,

Alternatively, the user may choose to weight models based on their observed performance $\mathrm{Perf}$ in previous years measured by the reciprocal of mean absolute percent error or root mean square error.

Giovanni Petris (2010). An R Package for Dynamic Linear Models. Journal of Statistical Software, 36(12), 1-16. URL https://www.jstatsoft.org/v36/i12/.

Petris, Petrone, and Campagnoli. Dynamic Linear Models with R. Springer (2009).