Process and sampling variance within fisheries stock assessment models: estimability, likelihood choice, and the consequences of incorrect specification

Abstract

Abstract Increasingly, mixed-effect fishery stock assessment models are being developed where deviations about functional forms of different processes are modelled as random effects and the extent of variance is estimated internal to the model. Concurrently, sampling variance parameters associated with likelihoods for fitting composition data within fisheries assessments are more often being estimated internal to the model as well. We examine the performance of stock assessment models when multiple process variance and sampling variance terms are simultaneously estimated within assessment models. We specifically examine how assessment performance is affected by the choice of composition likelihood, the degree of overdispersion in composition data, overparameterization, and modelling variation on the wrong process. In doing so, we build a simulation containing overdispersion and correlations in composition data, directional variation in catchability and/or selectivity, and estimation models which include random effects and composition likelihoods with theoretically estimable variances. Results suggest that with standard data available in fisheries assessments, process variance parameters associated with some commonly employed methods and sampling variance parameters can be simultaneously estimated internal to an assessment, and performance greatly improves with increased composition data. Our results also suggest little downside to overparameterization of selectivity and catchability when the true process is not time-varying, which largely agrees with previous research. However, when a process is truly time-varying and the assessment models time-variation on a different process, namely when selectivity is time-varying and instead natural mortality is modelled as potentially time-varying, we find a risk of severe increases in bias and decreases in confidence interval coverage for assessed quantities. This bias and decrease in coverage could, however, be partially mitigated by also modelling time-variation on the correct process.