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.

混合地理加权回归（MGWR）模型是用于建模回归关系的有用工具，其中某些解释变量对响应变量的影响是全局的，而其他解释变量的影响在空间上是变化的。MGWR模型的现有估计方法假定模型误差为同方差。但是，异方差在地理参考数据中非常常见，并且忽略异方差可能会导致系数估计的效率损失。本文提出了一种用于异方差MGWR模型的重新加权估计方法，该方法通过利用自适应带宽的核方法估计模型误差的方差函数，并基于加权观测值重新估计系数。仿真研究表明，该方法可以显着提高估计效率，特别是对于常数系数而言。给出了一个基于都柏林选民投票率数据的真实示例，以演示该方法的应用。