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J Geograph Syst (2005) 7: 161187DOI: 10.1007/s10109-005-0155-6ORIGINAL PAPERDavid Wheeler Michael TiefelsdorfMulticollinearity and correlation
among local regression coefcients
in geographically weighted regressionReceived: 25 October 2004 / Accepted: 21 February 2005
Springer-Verlag 2005Abstract Present methodological research on geographically weighted
regression (GWR) focuses primarily on extensions of the basic GWR
model, while ignoring well-established diagnostics tests commonly used in
standard global regression analysis. This paper investigates multicollinearity issues surrounding the local GWR coecients at a single location
and the overall correlation between GWR coecients associated with two
dierent exogenous variables. Results indicate that the local regression
coecients are potentially collinear even if the underlying exogenous
variables in the data generating process are uncorrelated. Based on these
ndings, applied GWR research should practice caution in substantively
interpreting the spatial patterns of local GWR coecients. An empirical
disease-mapping example is used to motivate the GWR multicollinearity
problem. Controlled experiments are performed to systematically explore
coecient dependency issues in GWR. These experiments specify global
models that use eigenvectors from a spatial link matrix as exogenous
variables.This study was supported by grant number 1 R1 CA95982-01, Geographic-Based
Research in Cancer Control and Epidermiology, from the National Cancer Institute.
The author thank the anonymous reviewers and the editor for their helpful comments.D. Wheeler (&)Department of Geography, The Ohio State University,
1036 Derby Hall, Columbus, OH 43210, USAE-mail: [email protected]. TiefelsdorfSchool of Social Sciences,University of Texas at Dallas, Richardson, TX 75083, USA
E-mail: [email protected] D. Wheeler and M. TiefelsdorfKeywords Geographically weighted regression Multicollinearity
Local regression diagnostics Spatial eigenvectors Experimental
spatial design1 IntroductionGeographically weighted regression (GWR) aims at identifying spatial heterogeneities in regression models of geo-referenced data. The spatial variability of the estimated local regression coecients is usually examined to
determine whether the underlying data generating process exhibits spatial
heterogeneities or local deviations from a global regression model. A common procedure is to map the spatial GWR coecient pattern associated with
each exogenous variable. This approach, however, ignores potential dependencies among the local regression coecients associated with dierent
exogenous variables. Attention in this paper centers on these potential
dependencies among the local coecients. They can be expressed either as
the correlation between pairs of local regression coecients at one location or
as the correlation between two overall sets of local coecient estimates
associated with two exogenous...