Links, comparisons and extensions of the geographically weighted regression model when used as a spatial predictor

  • Paul Harris
  • Chris Brunsdon
  • A. Stewart Fotheringham
Original Paper


In this study, we link and compare the geographically weighted regression (GWR) model with the kriging with an external drift (KED) model of geostatistics. This includes empirical work where models are performance tested with respect to prediction and prediction uncertainty accuracy. In basic forms, GWR and KED (specified with local neighbourhoods) both cater for nonstationary correlations (i.e. the process is heteroskedastic with respect to relationships between the variable of interest and its covariates) and as such, can predict more accurately than models that do not. Furthermore, on specification of an additional heteroskedastic term to the same models (now with respect to a process variance), locally-accurate measures of prediction uncertainty can result. These heteroskedastic extensions of GWR and KED can be preferred to basic constructions, whose measures of prediction uncertainty are only ever likely to be globally-accurate. We evaluate both basic and heteroskedastic GWR and KED models using a case study data set, where data relationships are known to vary across space. Here GWR performs well with respect to the more involved KED model and as such, GWR is considered a viable alternative to the more established model in this particular comparison. Our study adds to a growing body of empirical evidence that GWR can be a worthy predictor; complementing its more usual guise as an exploratory technique for investigating relationships in multivariate spatial data sets.


Heteroskedastic Local uncertainty Relationship nonstationarity 



Research presented in this paper was funded by a Strategic Research Cluster grant (07/SRC/I1168) by the Science Foundation Ireland under the National Development Plan. The authors gratefully acknowledge this support. Thanks are also due to the first author’s PhD studentship and S. Juggins at Newcastle University; and to M. Kernan at University College London for providing the case study data.


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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Paul Harris
    • 1
  • Chris Brunsdon
    • 2
  • A. Stewart Fotheringham
    • 1
  1. 1.National Centre for GeocomputationNational University of IrelandMaynoothIreland
  2. 2.Department of GeographyUniversity of LeicesterLeicesterUK

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