Bayesian logistic mixed-effects modelling of transect data: relating red tree coral presence to habitat characteristics

Abstract

Abstract The collection of continuous data on transects is a common practice in habitat and fishery stock assessments; however, the application of standard regression models that assume independence to serially correlated data is problematic. We show that generalized linear mixed models (GLMMs), i.e. generalized linear models for longitudinal data, that are normally used for studies performed over time can also be applied to other types of clustered or serially correlated data. We apply a specific GLMM for longitudinal data, a hierarchical Bayesian logistic mixed-effects model (BLMM), to a marine ecology dataset obtained from submersible video recordings of the seabed on transects at two sites in the Gulf of Alaska. The BLMM was effective in relating the presence of red tree corals (Primnoa pacifica; i.e. binary data) to habitat characteristics: the presence of red tree corals is highly associated with bedrock as the primary substrate (estimated odds ratio 9–19), high to very high seabed roughness (estimated odds ratio 3–5), and medium to high slope (estimated odds ratio 2–3). The covariate depth was less important at the sites. We also demonstrate and compare two methods of model checking: full and mixed posterior predictive assessments, the latter of which provided a more realistic assessment, and we calculate the variance partition coefficient for reporting the variation explained by multiple levels of the hierarchical model.