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

Geographically weighted regression (GWR) is a way of exploring spatial nons tationarity by calibrating a multiple regression model which allows differe nt relationships to exist at different points in space. Nevertheless, forma l testing procedures for spatial nonstationarity have not been developed si nce the inception of the model. In this paper the authors focus mainly on t he 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 thei r approximated distributions are investigated. The work makes it possible t o test spatial nonstationarity in a conventional statistical manner. To sub stantiate the theoretical arguments, some simulations are run to examine th e power of the statistics for exploring spatial nonstationarity and the res ults are encouraging. To streamline the model, a stepwise procedure for cho osing important independent variables is also formulated. In the last secti on, a prediction problem based on the GWR model is studied, and a confidenc e interval for the true value of the dependent variable at a new location i s also established. The study paves the path for formal analysis of spatial nonstationarity on the basis of the GWR model.