Distribution-free regression model selection with a nested spatial correlation structure

In spatial regression analysis, a suitable specification of the mean regression model is crucial for unbiased analysis. Also, to enhance statistical efficiency of the mean regression analysis, we need to suitably account for the underlying spatial correlation structure. In this paper, we focus on selection of an appropriate mean model in spatial regression analysis under a general anisotropic nested correlation structure considered in Adegboye et al. (2018). We propose a distribution-free model selection criterion, called the Spatial Information Criterion (SIC), which is an estimate of the weighted mean squared error for predicting the response variable, and relies on assumptions only for the first two moments of the spatial response data. The simulations under the settings of covariate selection reveal that the SIC performs well for covariate selection in the mean model regardless of the correlation structure is nested/non-nested (multi-source or not), isotropic/anisotropic (direction-dependent or not). Also, the SIC accommodates both continuous and count response data. We illustrate the utility of the proposed method by a real data application concerning the predictive regression model for the fine particulate matter (PM_2.5) concentration.