Bayesian analysis of crossclassified spatial data with autocorrelation.

We address the development of methods for analyzing crossclassified categorical data that are spatially autocorrelated. We first extend the autologistic model to accommodate two variables. Two bivariate autologistic models are constructed, namely a two-step model and a symmetric model. Importance sampling is used to approximate the complex normalizing factors that arise in these models, and Markov chain Monte Carlo techniques are used to generate simulations of posterior distributions. The resulting models then are expanded to accommodate trend surfaces and directional effects. Simulation studies and real data are used to illustrate this method.