|Document Type:||Journal Article|
|Title:||Accounting for space-time interactions in index standardization models|
|Author:||James T. Thorson, E. J. Ward|
|Keywords:||index standardization,mixed-effects model,posterior predictive score,deviance information criterion,Bayesian model|
Scientific survey data are used to estimate abundance trends for fish populations worldwide, and are frequently analyzed using delta-generalized linear mixed models (delta-GLMMs). Delta-GLMMs incorporate information about both the probability of catch being non-zero (catch probability) and the expected value for non-zero catches (catch rates). They generally incorporate year as a main effect, and frequently account for spatial strata or covariates. Many existing delta-GLMMs do not account for random or systematic differences in catch probability or rates in particular combinations of spatial strata and year (i.e. space-time interactions), and do not recognize potential correlation between catch probability and rates. We therefore develop a novel Bayesian delta-GLMM that estimates correlations between catch probability and rates, and compare it with either (a) ignoring year-strata interactions, (b) modeling year-strata interactions as fixed effects, or (b) estimating year-strata interactions in catch probability or rates as independent random effects. These four models are fitted to bottom trawl survey data for 28 species of the U.S. West Coast. Model selection using posterior predictive scores indicates that random strata-year interactions are supported for the majority (22) of species. The posterior median of the correlation is positive for the majority (19) of species, including all 5 for which the posterior distribution is significantly different from zero. Additionally, the speed of Bayesian estimation is improved 3-4 fold even when the median posterior correlation is near zero. However, estimating this correlation has little impact on resulting abundance indices or confidence intervals. We therefore propose that this model is useful in distinguishing spatial patterns in survey data, particularly for datasets longer than our case study (9 years), but do not believe that is will have a large impact on index standardization of the West Coast bottom trawl dataset.