GWmodel: AnRPackage for Exploring Spatial Heterogeneity Using Geographically Weighted Models

Isabella Gollini,Binbin Lu,Paul Harris,Martin Charlton,Christopher Brunsdon

doi:10.18637/jss.v063.i17

Abstract

Spatial statistics is a growing discipline providing important analytical techniques in a wide range of disciplines in the natural and social sciences. In the R package GWmodel we present techniques from a particular branch of spatial statistics, termed geographically weighted (GW) models. GW models suit situations when data are not described well by some global model, but where there are spatial regions where a suitably localized calibration provides a better description. The approach uses a moving window weighting technique, where localized models are found at target locations. Outputs are mapped to provide a useful exploratory tool into the nature of the data spatial heterogeneity. Currently, GWmodel includes functions for: GW summary statistics, GW principal components analysis, GW regression, and GW discriminant analysis; some of which are provided in basic and robust forms.

Highlights

Spatial statistics provides important analytical techniques for a wide range of disciplines in the natural and social sciences, where spatial data sets are routinely collected
Notable geographically weighted (GW) models include: GW summary statistics (Brunsdon, Fotheringham, and Charlton 2002); GW principal components analysis (GW Principal components analysis (PCA), Fotheringham, Brunsdon, and Charlton 2002; Lloyd 2010a; Harris, Brunsdon, and Charlton 2011a); GW regression (Brunsdon, Fotheringham, and Charlton 1996, 1998, 1999; Leung, Mei, and Zhang 2000; Wheeler 2007); GW generalized linear models (Fotheringham et al 2002; Nakaya, Fotheringham, Brunsdon, and Charlton 2005); GW discriminant analysis (Brunsdon, Fotheringham, and Charlton 2007); GW variograms (Harris, Charlton, and Fotheringham 2010a); GW regression kriging hybrids (Harris and Juggins 2011) and GW visualization techniques (Dykes and Brunsdon 2007). Many of these GW models are included in the R (R Core Team 2014) package GWmodel that we describe in this paper
Collinearity is potentially more of an issue in GW regression because: (i) its effects can be more pronounced with the smaller spatial samples used in each local estimation and (ii) if the data are spatially heterogeneous in terms of its correlation structure, some localities may exhibit collinearity while others may not

Summary

Introduction

Spatial statistics provides important analytical techniques for a wide range of disciplines in the natural and social sciences, where (often large) spatial data sets are routinely collected. Collinearity is potentially more of an issue in GW regression because: (i) its effects can be more pronounced with the smaller spatial samples used in each local estimation and (ii) if the data are spatially heterogeneous in terms of its correlation structure, some localities may exhibit collinearity while others may not. In both cases, collinearity may be a source of problems in GW regression even when no evidence is found for collinearity in the global model (Wheeler and Tiefelsdorf 2005; Wheeler 2007, 2013a). Simulation studies have indicated that in the presence of collinearity, GW regression may find patterns in the coefficients where no patterns are present (Wheeler and Tiefelsdorf 2005; Paez, Farber, and Wheeler 2011)

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Discussion

Conclusion