A Route Map for Successful Applications of Geographically Weighted Regression

Alexis Comber,Paul Harris,Richard Harris,Binbin Lu,Christopher Brunsdon,Martin Charlton,Tomoki Nakaya,Daisuke Murakami,Yihe Lü,Yunqiang Wang,Guanpeng Dong

doi:10.1111/gean.12316

Abstract

Geographically Weighted Regression (GWR) is increasingly used in spatial analyses of social and environmental data. It allows spatial heterogeneities in processes and relationships to be investigated through a series of local regression models rather than a single global one. Standard GWR assumes that relationships between the response and predictor variables operate at the same spatial scale, which is frequently not the case. To address this, several GWR variants have been proposed. This paper describes a route map to decide whether to use a GWR model or not, and if so which of three core variants to apply: a standard GWR, a mixed GWR or a multiscale GWR (MS‐GWR). The route map comprises 3 primary steps that should always be undertaken: (1) a basic linear regression, (2) a MS‐GWR, and (3) investigations of the results of these in order to decide whether to use a GWR approach, and if so for determining the appropriate GWR variant. The paper also highlights the importance of investigating a number of secondary issues at global and local scales including collinearity, the influence of outliers, and dependent error terms. Code and data for the case study used to illustrate the route map are provided.

Highlights

This article provides guidance for successful applications of geographically weighted regression (GWR), a method of spatial analysis first proposed by Brunsdon and Fotheringham (1996)
Analyst A could have chosen a MS-GWR but the local differences in regression relationships with those of a MX-G WR were small, which were reflected in the AICc measures in this case (1,065.9 for MX-GWR and 1,050.4 for MS-GWR)
Analyst B experimented with a standard GWR based on the loose similarity of the MS-G WR bandwidths and the small differences in AICc between GWR forms (1,272.3 for standard GWR and 1,264.4 for MS-GWR), but standard GWR resulted in different local inferences where it identified fewer significant regression relationships and MS-GWR was retained

Summary

Introduction

This article provides guidance for successful applications of geographically weighted regression (GWR), a method of spatial analysis first proposed by Brunsdon and Fotheringham (1996). GWR provides measures of process heterogeneity— geographical variation in data relationships—through the generation of mappable and varying regression coefficients, and associated statistical inference. It has been extensively applied in a wide variety of scientific and socio-scientific disciplines, such as environmental health (e.g., Yoneoka and Saito 2016), landscape ecology (e.g., Zhang, Bi, and Cheng 2004), soil quality (e.g., Song et al 2016), air quality (e.g., You et al 2015), water quality (e.g., Sun, Guo, and Liu 2014), remote sensing (e.g., Foody 2003), disease patterns (e.g., Brunton et al 2017), urban studies (e.g., Huang and Yuan 2019), and housing markets (e.g., Yu and Wei 2007)

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Conclusion