Testing spatial heteroscedasticity in mixed geographically weighted regression models

Abstract

Spatial homoscedasticity of the error term is commonly assumed in mixed geographically weighted regression analysis. In many practical situations, however, rarely can we know a priori whether the error term is homoscedastic or not. Therefore, it is necessary to first detect the spatial heteroscedasticity of the error term before the mixed geographically weighted regression model is used. In this paper, a statistic is constructed based on the square root of the absolute value of the residuals obtained by the two step estimation. The three moment χ2 approximation is applied to compute the p value of the test. Furthermore, simulation results show that the proposed test method has high accuracy and satisfactory power in detecting spatial heteroscedasticity, even when the model errors follow non-normal distributions. A real-world data set is analysed to demonstrate the application of the proposed test method and the paper is ended with a conclusion.