Spatially varying coefficient models using reduced-rank thin-plate splines

• Published in: Spatial statistics Vol. 51; p. 100654
• Main Authors: Fan, Yu-Ting, Huang, Hsin-Cheng
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.10.2022
• Subjects: Cross-validation; Generalized linear model; Geographically weighted regression; Log-normal regression; Model selection; Multiresolution spline basis function; Multiresolution spline basis function; Generalized linear model; Model selection; Log-normal regression; Cross-validation; Geographically weighted regression
• ISSN: 2211-6753; 2211-6753
• DOI: 10.1016/j.spasta.2022.100654

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.