Dimension Reduction and Alleviation of Spatial Confounding for Non-Gaussian Spatial Models

• Activity Number: 21
• Type: Topic Contributed
• Date/Time: Sunday, July 31, 2011 : 2:00 PM to 3:50 PM
• Sponsor: ENAR
• Author(s): Murali Haran*+ and John Hughes
• Companies: Penn State University and Penn State University
• Keywords: Spatial generalized linear mixed models ; Gaussian Markov random fields ; spatial binary data ; lattice models

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 problems. When fitting spatial regressions for such data one needs to account for dependence appropriately both for reliable inference regarding the regression coefficients as well as for accurate predictions. Spatial generalized linear mixed models (SGLMMs) are very popular and flexible approaches for modeling such data but they suffer from two major shortcomings: (i) the regression coefficient estimates obtained in SGLMMs are often uninterpretable due to confounding with the spatial random effects, (ii) the number of spatial random effects grows as the data set increases in size, making fully Bayesian inference for such models computationally infeasible in many cases. We propose a new sparse reparameterization of the SGLMM that simultaneously addresses both these issues by greatly reducing the dimension of the spatial random effects and providing more interpretable regression parameter estimates. We illustrate the application of our approach to both simulated and real data sets.