Markov Chain Monte Carlo for Autologistic Regression Models with Application to the Distribution of Plant Species

In this paper, we explore using autologistic regression models for spatial binary data with covariates. Autologistic regression models can handle binary responses exhibiting both spatial correlation and dependence on covariates. We use Markov chain Monte Carlo (MCMC) to estimate the parameters in these models. The distributional behavior of the MCMC maximum likelihood estimates (MCMC MLEs) is studied via simulation. We find that the MCMC MLEs are approximately normally distributed and that the MCMC estimates of Fisher information may be used to estimate the variance of the MCMC MLEs and to construct confidence intervals. Finally, we illustrate by example how our studies may be applied to model the distribution of plant species.