On estimation in binary autologistic spatial models

There is a large and increasing literature in methods of estimation for spatial data with binary responses. The goal of this article is to describe some of these methods for the autologistic spatial model, and to discuss computational issues associated with them. The main way we do this is via illustration using a spatial epidemiology data set involving liver cancer. We first demonstrate why maximum likelihood is not currently feasible as a method of estimation in the spatial setting with binary data using the autologistic model. We then discuss alternative methods, including pseudo likelihood, generalized pseudo likelihood, and Monte Carlo maximum likelihood estimators. We describe their asymptotic efficiencies and the computational effort required to compute them. These three methods are applied to the data set and compared in a simulation experiment.