Regression Kriging versus Geographically Weighted Regression for Spatial Interpolation

Abstract

If spatial dependence and/or spatial heterogeneity are taken into account in the process of spatial interpolation, the prediction process can be named local-spatial prediction. Geographically weighted regression is a type of local-spatial prediction models since methodologically it incorporates spatial heterogeneity into a regression model. From the standpoint of spatial interpolation, regression kriging is presented as another local-spatial prediction model that incorporates local-spatial dependence, association between response and auxiliary variables, and the unbiased estimation with minimized variance into an interpolation process. The methodologies of regression kriging and geographically weighted regression are summarized to indicate how local-spatial correlation, spatial heterogeneity, and non-spatial correlation and are incorporated into interpolation process. This paper points out regression kriging applies the local variation of spatial dependence to regression parameter estimation and combines the estimated regression model with residual kriging considering spatial autocorrelation in residuals as a hybrid local-spatial interpolator. Using a raster data with two types of sampling approaches, this study examines and compares the performance of regression kriging and geographically weighted regression. The empirical examples indicate that both regression kriging and geographically weighted regression are powerful local-spatial prediction models, but regression kriging can be better in capturing the spatial structure of the original data.