Efficient estimation of heteroscedastic mixed geographically weighted regression models

Mixed geographically weighted regression (MGWR) models are a useful tool to model a regression relationship where the impact of some explanatory variables on the response variable is global and that of the others is spatially varying. The existing estimation methods for MGWR models assume that the model errors are homoscedastic. However, heteroscedasticity is very common in geo-referenced data and ignoring heteroscedasticity may cause efficiency loss on the coefficient estimates. In this paper, we propose a re-weighting estimation method for heteroscedastic MGWR models, in which the variance function of the model errors is estimated by the kernel method with an adaptive bandwidth and the coefficients are re-estimated based on the weighted observations. The simulation study shows that the proposed method can substantially improve the estimation efficiency especially for the constant coefficients. A real-world example based on the Dublin voter turnout data is given to demonstrate the application of the proposed method.