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Abstract:
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Spatial patterns can be generated by processes that are dynamic in space and time. Analyzing spatial data often requires modeling dependencies created by a dynamic process. In many applications, the generalized linear mixed model (GLMM) is used with a random effect to account for such dependence. Covariates are often included as fixed effects in a GLMM and may be collinear with the random effects. When using the GLMM, collinearity between covariates and random effects can complicate the implementation and effect inference. We demonstrate the potential for confounding in traditional spatial random effects GLMMs and propose a constructive approach to account for spatial dependence that incorporates scientific knowledge of the spatio-temporal process. Our approach relies on a dynamic spatio-temporal model (e.g., stochastic partial differential equation model) that explicitly incorporates spatial covariates to account for dependence. We illustrate our approach using a spatially varying ecological diffusion model to understand risk factors associated with chronic wasting disease in white-tailed deer from Wisconsin, USA.
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