Assessing likelihoods for fitting composition data within stock assessments, with emphasis on different degrees of process and observation error

Abstract

Fisheries stock assessments have traditionally modeled age and size composition data using the multinomial likelihood, however the multinomial cannot appropriately account for the correlations and overdispersion that exist in the observed data or in the model residuals. Not accounting for these phenomena can affect assessment performance. Methods to remedy this have included down-weighting composition data within assessments either arbitrarily or by using iterative re-weighting algorithms, and by using alternative likelihoods to the multinomial that can be weighted within the assessment. Iteratively re-weighting composition data in stock assessments is inefficient and does not ultimately account for correlations in the residuals, and alternative likelihoods for composition data have not all been evaluated using stock assessment simulations. To evaluate the performance of alternative likelihoods in fitting composition data, we first developed a spatially explicit age-structured operating model to simulate correlation structure observed in real composition data. We then fit spatially aggregated assessment models to the simulated data and assessed the performance of various formulations of composition likelihoods (Multinomial, Robust Multinomial, Dirichlet, Dirichlet-multinomial, and Logistic-normal) in estimating stock dynamics and quantities of management interest. Results suggest that the degree of process error (combining both process variation and model misspecification) and the sample size of the composition data have a larger effect on the relative performance of different likelihoods than the degree of overdispersion and correlations in composition data. When the composition sample size was moderate to large and there existed at least a moderate amount of process error, the Logistic-normal likelihood performed best. When the sample size was small, or when process error was non-existent or negligible, the Dirichlet-multinomial likelihood performed best.