A Statistical Approach to Estimating Multinomial Effective Sample Size for Stock Assessment Models

Stock assessment models infer fish population dynamics through the match between observed data and model predictions.  In catch-at-age and catch-at-size models, these data often include proportions-at-age (or size) in the fishery or survey catch.  The evaluation of the match with predictions for these composition data is often made using the multinomial likelihood, which requires specification of the effective sample size (ESS).  ESS weights these composition data relative to other data being fit, and is not an estimable parameter within a model.  Its value is typically less than the actual sample size because of factors such as clustered sampling designs.  A common approach for specifying ESS is to iteratively re-fit the model until ESS converges, determining ESS after each fit so that standardized residual variance is "correct."  We propose an extension of such methods.  Instead of analytically solving for the “correct” ESS, we estimate ESS for each year by statistically modeling its distribution, with an expected value a function of the annual level of sampling.  This approach provides more flexibility, because it allows estimation of multiple parameters relating ESS to measures of sampling.  We illustrate this approach through application to Lake Whitefish assessments from the Laurentian Great Lakes.