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

Dimension Reduction and Alleviation of Confounding for Spatial Generalized Linear Mixed Models