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

TL;DR

This paper introduces a new parameterization for spatial generalized linear mixed models that reduces confounding and computational complexity, improving inference for non-Gaussian spatial data like disease counts and ecological binary data.

Contribution

The authors propose a novel parameterization of SGLMMs that alleviates spatial confounding and reduces the dimension of spatial random effects, enhancing interpretability and computational efficiency.

Findings

Effective in simulated binary, count, and Gaussian datasets

Improves inference accuracy by reducing confounding effects

Speeds up computation for large spatial datasets

Abstract

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.