A Spatial Filtering Specification for the Autologistic Model

The autologistic model describes binary correlated data; its spatial version describes georeferenced binary data exhibiting spatial dependence. The conventional specification of a spatial autologistic model involves difficult-to-nearly-impossible computations to ensure that appropriate sets of probabilities sum to 1. Work summarized here accounts for spatial autocorrelation by including latent map pattern components as covariates in a model specification. These components derive from the surface zonation scheme used to aggregate attribute data, to construct a geographic weights matrix, and to evaluate geographic variability. The illustrative data analysis is based upon field plot observations for the pathogen Phytophthora capsici that causes disease in pepper plants. Results are compared with pseudolikelihood and Markov chain Monte Carlo estimation techniques, both for the empirical example and for two simulation experiments associated with it. The principal finding is that synthetic map pattern variables, which are eigenvectors computed for a geographic weights matrix, furnish an alternative, successful way of capturing spatial dependency effects in the mean response term of a logistic regression model, avoiding altogether the need to use other than traditional standard techniques to estimate model parameters.