Selection of the Bandwidth Matrix in Spatial Varying Coefficient Models to Detect Anisotropic Regression Relationships

Abstract

The commonly used Geographically Weighted Regression (GWR) fitting method for a spatial varying coefficient model is to select a bandwidth h for the geographic location (u, v), and assign the same weight to the two dimensions. However, spatial data usually present anisotropy. The introduction of a two-dimensional bandwidth matrix not only gives weight from two dimensions separately, but also increases the direction of kernel smoothness. The adaptive bandwidth matrix is more flexible. Therefore, in this paper, a two dimensional bandwidth matrix is introduced into the spatial varying coefficient model for parameter estimation. Through simulation experiments, the results obtained under the adaptive bandwidth matrix are compared with those obtained under the global bandwidth matrix, indicating the effectiveness of introducing the adaptive bandwidth matrix.