Variable selection for spatial latent predictors under Bayesian spatial model

The problem of variable selection is encountered in model fitting with unobserved spatial predictors at the sites where outcomes are measured. The variability of the interpolated predictors at outcome sites results in potential problems of variable selection and averaging the results across different datasets. A Bayesian spatial model is developed to tackle this issue. By sampling the latent spatial predictors and selecting the spatial and non-spatial predictors using stochastic search variable selection Gibbs sampling algorithm, our approach allows for uncertainty of the predictors including the interpolated predictors. The approach is evaluated and illustrated through a simulated data example and an application to mental retardation and developmental delay in a Medicaid population in South Carolina with samples of soil chemistry.