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On estimation in binary autologistic spatial models. (English) Zbl 1088.62069
Summary: There is a large and increasing literature on 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.

MSC:
62H11 Directional data; spatial statistics
62P10 Applications of statistics to biology and medical sciences; meta analysis
62M30 Inference from spatial processes
65C05 Monte Carlo methods
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