Bayesian and frequentist approaches to multinomial count models in ecology

Abstract

Multinomial count data are common in trophic ecology, spatial ecology, and community ecology. Compared to generalized linear models (GLMs) for univariate data, fewer statistical programs have been developed for the multivariate counterpart of GLMs. Studies of spatiotemporal community dynamics and spatial ecology on large spatial scales may generate large or big data on compositional counts or proportions. Fast, reliable computational methods can promote applications of multivariate generalized linear models (MGLMs) in predictive ecology and ecological informatics. The main objective of this study was to build Dirichlet-multinomial (D-M) models for compositional counts using frequentist's maximum likelihood estimation (MLE) with template model builder (TMB), full Bayesian estimation with programs JAGS and Stan, and variational Bayes in Stan. Bayesian and frequentist D-M models were applied to the compositional counts of radio telemetry locations of ring-necked pheasants (Phasianus colchicus) and American beaver (Castor canadensis) in different habitat-cover types to estimate habitat selection index. Bayesian D-M models with JAGS and Stan produced similar estimates as TMB programs. However, TMB programs ran a few hundred times faster than the Bayesian models. Template model builder and Stan are flexible in building complex statistical models and can accommodate a large number of parameters and random effects. The joint use of TMB and Stan may help develop MGLMs and multivariate generalized linear mixed models for large ecological data.