  Non-gaussian spatial data are very common in many disciplines. For instance,
count data are common in disease mapping, and binary data are common in
ecology. When fitting spatial regressions for such data, one needs to account
for dependence to ensure reliable inference for the regression coefficients.
The spatial generalized linear mixed model (SGLMM) offers a very popular and
flexible approach to modeling such data, but the SGLMM suffers from three major
shortcomings: (1) uninterpretability of parameters due to spatial confounding,
(2) variance inflation due to spatial confounding, and (3) high-dimensional
spatial random effects that make fully Bayesian inference for such models
computationally challenging. We propose a new parameterization of the SGLMM
that alleviates spatial confounding and speeds computation by greatly reducing
the dimension of the spatial random effects. We illustrate the application of
our approach to simulated binary, count, and Gaussian spatial datasets, and to
a large infant mortality dataset.
