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

• Activity Number: 614
• Type: Contributed
• Date/Time: Thursday, August 2, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): John Hughes and Murali Haran
• Companies: University of Minnesota and Penn State University
• Keywords: dimension reduction ; generalized linear model ; harmonic analysis ; mixed model ; regression ; spatial statistics

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 two major shortcomings: (1) variance inflation due to spatial confounding, and (2) 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.