A flexible Bayesian nonconfounding spatial model for analysis of dispersed count data

In employing spatial regression models for counts, we usually meet two issues. First, the possible inherent collinearity between covariates and the spatial effect could lead to misleading inferences. Second, real count data usually reveal over- or under-dispersion where the classical Poisson model is not appropriate to use. We propose a flexible Bayesian hierarchical modeling approach by joining nonconfounding spatial methodology and a newly reconsidered dispersed count modeling from the renewal theory to control the issues. Specifically, we extend the methodology for analyzing spatial count data based on the gamma distribution assumption for waiting times. The model can be formulated as a latent Gaussian model, and consequently, we can carry out the fast computation by using the integrated nested Laplace approximation method. We examine different popular approaches for handling spatial confounding and compare their performances in the presence of dispersion. Two real applications from a crime study against women in India as well as stomach cancer incidences in Slovenia motivate the suggested methods. We also perform a simulation study to understand the proposed approach's merits better. Supplementary Materials for this article are available.