  In analyses of spatially-referenced data, researchers often have one of two
goals: to quantify relationships between a response variable and covariates
while accounting for residual spatial dependence or to predict the value of a
response variable at unobserved locations. In this second case, when the
response variable is categorical, prediction can be viewed as a classification
problem. Many classification methods either ignore response-variable/covariate
relationships and rely only on spatially proximate observations for
classification, or they ignore spatial dependence and use only the covariates
for classification. The Bayesian spatial generalized linear (mixed) model
offers a tool to accommodate both spatial and covariate sources of information
in classification problems. In this paper, we formally define spatial
classification rules based on these models. We also take a close look at two of
these models that have been proposed in the literature, namely the probit
versions of the spatial generalized linear model (SGLM) and the Bayesian
spatial generalized linear mixed model (SGLMM). We describe the implications of
the seemingly slight differences between these models for spatial
classification and explore the issue of robustness to model misspecification
through a simulation study. We also provide an overview of alternatives to the
SGLM/SGLMM-based classifiers and illustrate the various methods using
satellite-derived land cover data from Southeast Asia.

Methodology