Autologistic Regression Models for Spatio-Temporal Binary Data

Binary data on a spatial lattice are often encountered in environmental and ecological studies. Spatial statistical methods have been developed for modeling spatial binary responses and their relations to covariates while properly accounting for spatial correlation. In this chapter, we review autologistic models in the class of Markov random fields that model spatial dependence via autoregression and consider extensions to autologistic regression models for spatio-temporal binary data. In particular, the introduction of autoregression in space and time results in an unknown normalizing constant in the likelihood function, which makes estimation and statistical inference challenging. We describe 368several approaches to the inference for spatio-temporal autologistic regression models and illustrate them by an ecological data example.