Dealing with missing covariate data in fishery stock assessment models

Abstract

Covariates are now commonly used in fisheries stock assessment models to provide additional information about model parameters, but their use can be complicated by missing values. A wide range of covariates have been used (e.g. environment, disease, predation, food, pollutants) to model different processes (e.g. recruitment, natural mortality, growth, catchability). Several approaches are available to deal with missing covariate values. We illustrate a likelihood based approach to deal with missing covariate data when including covariates into fisheries stock assessment models. The method treats the missing covariate values as parameters from a random effects distribution. The parameters of the random effects distribution are estimated based on the observed values of the covariate. The true likelihood is implemented by integrating across the missing value random effect and, in our stock assessment example, a random effect for unexplained variation in recruitment using Laplace approximation. Simulation analysis is used to test the performance of the method and compare it to alternative approaches: (1) ignoring the covariate altogether, (2) ignoring the years with missing covariate values, (3) substituting the missing values with the mean of the observed values, and (4) estimating the missing values as free parameters. We apply the simulation analysis to a linear regression and a statistical catch-at-age stock assessment model. The simulation analysis results indicate that the random effects method for dealing with missing covariate data works moderately well, but it does not provide a substantial benefit over other less complex methods.