Objective Bayesian Model Selection for Spatial Hierarchical Models with Intrinsic Conditional Autoregressive Priors

We develop Bayesian model selection via fractional Bayes factors to simultaneously assess spatial dependence and select regressors in Gaussian hierarchical models with intrinsic conditional autoregressive (ICAR) random effects. Selection of covariates structure is difficult, as confounding creates a tension between fixed Researchers have commonly performed separately for effects models. Simultaneous methods relieve the researcher from arbitrarily fixing one these types while selecting other. Notably, approaches are limited. Our use allows under automatic reference priors parameters, which obviates need specify hyperparameters priors. also show equivalence two ICAR specifications derive minimal training size factor applied prior. perform simulation study performance our approach we compare results Deviance Information Criterion Widely Applicable Criterion. demonstrate that assigns low posterior probability when data truly independent reliably selects correct covariate highest within space. Finally, applications county-level median household income contiguous United States residential crime rates neighborhoods Columbus, Ohio.