Estimation of the mixed geographically weighted regression model based on the Minkowski distance

.The mixed geographically weighted regression model has been extensively studied both in its estimation and applications. However, in most existing research results of the model, the spatial weights are commonly computed based on the Euclidean distance, which is a straight-line distance metric. Considering the diversity of the sample data and the complexity of the geography, the Euclidean distance may be inappropriate. Thus, it is necessary to define an appropriate distance metric when calibrating a space model. In this article, a class of non Euclidean distance metrics – Minkowski distance, by varying its exponent parameter and the coordinate rotation, is used to compute the spatial weights in calibrating the mixed geographically regression model. Considering the fact that the two-step estimation procedure is less time-consuming and can obtain explicit expressions of the coefficients, we mainly focus on the performance of the two-step estimation method with Minkowski distance. Simulation results demonstrate that the proposed method has more robustness to the sample data and tends to obtain more accurate constant and varying coefficient estimates. A real-world dataset is analyzed to show the application of the proposed estimation method and the article is ended with a conclusion.