Testing for spatial autocorrelation among the residuals of the geographically weighted regression

Geographically weighted regression (GWR) is a useful technique for explorin g spatial nonstationarity by calibrating, for example, a regression model w hich allows different relationships to exist at different points in space. In this line of research, many spatial data sets have been successfully ana lyzed and some statistical tests for spatial variation have been developed. However, an important assumption in these studies is that the disturbance terms of the GWR model are uncorrelated and of common variance. Similar to the case in the ordinary linear regression, spatial autocorrelation can inv alidate the standard assumption of homoscedasticity of the disturbances and mislead the results of statistical inference. Therefore, developing some s tatistical methods to test for spatial autocorrelation is a very important issue. In this paper, two kinds of the statistical tests for spatial autoco rrelation among the residuals of the GWR model are suggested. Also, an effi cient approximation method for calculating the p-values of the test statist ics is proposed. Some simulations are run to examine the performances of th e proposed methods and the results are encouraging. The study not only make s it possible to test for spatial autocorrelation among the GWR residuals i n a conventional statistical manner, but also provides a useful means for m odel validation.