Accounting for space–time interactions in index standardization models

• Interactions between spatial strata and year are explored for index standardization.
• Random strata–year interactions can be estimated as correlated.
• Correlated strata–year interactions are supported and positive for several species.
• Correlated and uncorrelated strata–year interactions yield similar abundance indices.

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). Delta-GLMMs generally incorporate year as a main effect, and frequently account for spatial strata and/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 in random space–time interactions between catch probability and catch rates. We therefore develop a 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 (c) 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 off the U.S. West Coast. The posterior median of the correlation is positive for the majority (18) of species, including all five for which the posterior distribution has little overlap with zero. However, estimating this correlation has little impact on resulting abundance indices or credible intervals. We therefore conclude that the correlated random model will have a little impact on index standardization of the West Coast bottom trawl dataset. However, we propose that the correlated model can quickly identify correlations between occupancy probability and density, and provide our code to allow researchers to quickly identify whether such a correlation is likely to be significantly different from zero for their chosen data set.