The spatial random effects model is popular in analyzing spatially referenced data sets. The model includes spatially observed covariates and unobserved spatial random effects. If spatial confounding between covariates and random effects is ignored, parameter estimation and spatial prediction would be inaccurate. In this research, we focus on discussing the estimation of regression coefficients and the selection of covariates for spatial regression when existing unmeasured confounders. First, we introduce an adjusted estimation method for regression coefficients and the consequent spatial predictor in the presence of spatial confounding. From a prediction point of view, we then propose a generalized conditional Akaike information criterion to select a subset of covariates, resulting in satisfactory variable selection and spatial prediction. Statistical inferences of the proposed methodology are justified theoretically and numerically.
- Conditional information criterion
- mean squared prediction error
- restricted spatial regression
- spatial prediction
- variable selection