Autologistic regression analysis of spatial-temporal binary data via Monte Carlo maximum likelihood

This article considers logistic regression analysis of binary data that are measured on a spatial lattice and repeatedly over discrete time points. We propose a spatial-temporal autologistic regression model and draw statistical inference via maximum likelihood. Due to an unknown normalizing constant in the likelihood function, we use Monte Carlo to obtain maximum likelihood estimates of the model parameters and predictive distributions at future time points. We also use path sampling to estimate the unknown normalizing constant and approximate an information criterion for model assessment. The methodology is illustrated by the analysis of a dataset of mountain pine beetle outbreaks in western Canada.