Spatially Varying Coefficient Models: Testing for Spatial Heteroscedasticity and Reweighting Estimation of the Coefficients

Abstract

In the framework of the geographically weighted regression technique, spatial homoscedasticity of the model error term is a common assumption when a spatially varying coefficient model is calibrated to explore spatial nonstationarity of the regression relationship. In many real-world problems, however, this assumption cannot be guaranteed. In this study we first present a residual-based test method for detecting spatial heteroscedasticity of a spatially varying coefficient model. Then, we suggest a local linear smoothing procedure to estimate the variance function of the model error when heteroscedasticity exists, on which a reweighting estimation of the regression coefficients is derived. Some numerical experiments are conducted to evaluate the performance of the test and the gain in accuracy of the coefficient estimates by using the reweighting estimation method. The results demonstrate that the test method is powerful and that the reweighting estimation can improve the accuracy of the coefficient estimates, especially when strong heteroscedasticity exists in the model error term. Finally, a real-world dataset is analyzed to demonstrate the applications of the proposed test and estimation methods.