Spatially varying coefficient (SVC) regression models are concerned about regression for spatial data, where regression coefficients may vary in space. This paper proposes a new approach for SVC modeling by representing regression coefficients using a class of multiresolution spline basis functions in a generalized-linear model framework. The proposed method provides flexible and parsimonious representations for regression coefficients. It enables commonly used (generalized) linear-regression packages for estimation, testing, and constructing confidence levels. We develop a fast estimation algorithm that simultaneously performs variable selection, detects spatial heterogeneity for each variable, and determines its complexity. We provide numerical examples and an application to a real estate dataset to demonstrate the proposed method’s effectiveness.

空间变化系数 (SVC) 回归模型关注空间数据的回归，其中回归系数可能随空间变化。本文提出了一种新的 SVC 建模方法，通过在广义线性模型框架中使用一类多分辨率样条基函数表示回归系数。所提出的方法为回归系数提供了灵活和简约的表示。它支持用于估计、测试和构建置信水平的常用（广义）线性回归包。我们开发了一种快速估计算法，该算法同时执行变量选择，检测每个变量的空间异质性，并确定其复杂性。