Thorson, J.T. and E.J. Ward. 2013. Accounting for space-time interactions in index

standardization models. Fisheries Research,147:426:433

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.