Restricted spatial regression in practice: geostatistical models, confounding, and robustness under model misspecification. Issue 4 (18th February 2015)

• Record Type: Journal Article
• Authors: Hanks, Ephraim M.; Schliep, Erin M.; Hooten, Mevin B.; Hoeting, Jennifer A.
• Is Part Of: Environmetrics. Volume 26:Issue 4(2015:Jun.)
• Page Start: 243
• Page End: 254
• Publication Date: 2015-02-18
• Subjects: generalized linear mixed model -- spatial confounding -- random effects -- restricted regression; Environmental sciences -- Statistical methods -- Periodicals; 550.72
• DOI: 10.1002/env.2331
• Languages: English
• ISSNs: 1180-4009

Abstract

Abstract : In spatial generalized linear mixed models (SGLMMs), covariates that are spatially smooth are often collinear with spatially smooth random effects. This phenomenon is known as spatial confounding and has been studied primarily in the case where the spatial support of the process being studied is discrete (e.g., areal spatial data). In this case, the most common approach suggested is restricted spatial regression (RSR) in which the spatial random effects are constrained to be orthogonal to the fixed effects. We consider spatial confounding and RSR in the geostatistical (continuous spatial support) setting. We show that RSR provides computational benefits relative to the confounded SGLMM, but that Bayesian credible intervals under RSR can be inappropriately narrow under model misspecification. We propose a posterior predictive approach to alleviating this potential problem and discuss the appropriateness of RSR in a variety of situations. We illustrate RSR and SGLMM approaches through simulation studies and an analysis of malaria frequencies in The Gambia, Africa. Copyright © 2015 John Wiley & Sons, Ltd.