Geographically Weighted Regression

Abstract

Geographically weighted regression (GWR) was proposed in the geography literature to allow relationships in a regression model to vary over space. In contrast to traditional linear regression models, which have constant regression coefficients over space, regression coefficients are estimated locally at spatially referenced data points with GWR. The motivation for the introduction of GWR is the idea that a set of constant regression coefficients cannot adequately capture spatially varying relationships between covariates and an outcome variable. GWR is based on the appealing idea from locally weighted regression of estimating local models for curve fitting using subsets of observations centered on a focal point. GWR has been applied widely in diverse fields, such as ecology, forestry, geography, and regional science. At the same time, published work from several researchers has identified methodological issues and concerns with GWR and has questioned the application of the method for inferential analysis. One of the concerns with GWR is with strong correlation in estimated coefficients for multivariate regression terms, which makes interpretation of map patterns for individual terms problematic. The evidence in the literature suggests that GWR is a relatively simple and effective tool for spatial interpolation of an outcome variable and a more problematic tool for inferring spatial processes in regression coefficients. The more complex approach of Bayesian spatially varying coefficient models has been demonstrated to better capture spatial nonstationarity in regression coefficients than GWR and is recommended as an alternative for inferential analysis.