An empirical comparison of alternative likelihood formulations for composition data, with application to cobia and Pacific hake

Abstract

Fitting composition data within stock assessment models has historically utilized the multinomial likelihood, often with iterative reweighting algorithms to account for overdispersion due to sampling and process error. Recently, the Dirichlet-multinomial has been increasingly incorporated into assessments as a composition likelihood that can be internally weighted using an estimated overdispersion parameter. There exist two popular formulations of the Dirichlet-multinomial. Recent research has also suggested improved performance in assessments using the logistic-normal for composition data, specifically when the composition sample size is large. We evaluated the performance of two Dirichlet-multinomial formulations and the logistic-normal by incorporating them into assessments that differed greatly in sample sizes for composition data: cobia ( Rachycentron canadum) and Pacific hake ( Merluccius productus). We compared the likelihoods against one another using various model diagnostic criteria common in stock assessments. Overall, the linear formulation of the Dirichlet-multinomial outperformed the saturating formulation. At small sample sizes of the cobia assessment, the logistic-normal performed poorly. The comparison was more robust at large sample sizes of the Pacific hake assessment; however on balance, it seems prudent to proceed with the Dirichlet-multinomial.