Statistical tests for spatial nonstationarity based on the geographically weighted regression model

Geographically weighted regression (GWR) is a way of exploring spatial nonstationarity by calibrating a multiple regression model which allows different relationships to exist at different points in space. Nevertheless, formal testing procedures for spatial nonstationarity have not been developed since the inception of the model. In this paper the authors focus mainly on the development of statistical testing methods relating to this model. Some appropriate statistics for testing the goodness of fit of the GWR model and for testing variation of the parameters in the model are proposed and their approximated distributions are investigated. The work makes it possible to test spatial nonstationarity in a conventional statistical manner. To substantiate the theoretical arguments, some simulations are run to examine the power of the statistics for exploring spatial nonstationarity and the results are encouraging. To streamline the model, a stepwise procedure for choosing important independent variables is also formulated. In the last section, a prediction problem based on the GWR model is studied, and a confidence interval for the true value of the dependent variable at a new location is also established. The study paves the path for formal analysis of spatial nonstationarity on the basis of the GWR model.