Large variability and correlations among the coefficients obtained from the method of geographically weighted regression (GWR) have been identified in previous research. This is an issue that poses a serious challenge for the utility of the method as a tool to investigate multivariate relationships. The objectives of this paper are to assess: (1) the ability of GWR to discriminate between a spatially constant processes and one with spatially varying relationships; and (2) to accurately retrieve spatially varying relationships. Extensive numerical experiments are used to investigate situations where the underlying process is stationary and nonstationary, and to assess the degree to which spurious intercoefficient correlations are introduced. Two different implementations of GWR and cross-validation approaches are assessed. Results suggest that judicious application of GWR can be used to discern whether the underlying process is nonstationary. Furthermore, evidence of spurious correlations indicates that caution must be exercised when drawing conclusions regarding spatial relationships retrieved using this approach, particularly when working with small samples.
AkaikeH, 1973, “Information theory and an extension of the maximum likelihood principle”, in International Symposium on Information Theory Eds PetrovB NCsakiF (Akademiai Kiado, Budapest) pp 267–281.
BrundsdonCFotheringhamA SCharltonM E, 1996, “Geographically weighted regression: A method for exploring spatial nonstationarity”Geographical Analysis28281–298.
4.
ClevelandW S, 1979, “Robust locally weighted regression and smoothing of scatterplots”Journal of the American Statistical Association74823–836.
5.
ClevelandW SDevlinS J, 1988, “Locally weighted regression—an approach to regression-analysis by local fitting”Journal of the American Statistical Association83 (403) 596–610.
6.
FarberSPáezA, 2007, “A systematic investigation investigation of cross-validation in GWR model estimation: Empirical analysis and Monte Carlo simulations”Journal of Geographical Systems9371–396.
7.
FarberSYeatesM, 2006, “A comparison of localized regression models in a hedonic house price context”Canadian Journal of Regional Science29405–420.
8.
FarberSPáezAVolzE, 2009, “Topology and dependency tests in spatial and network autoregressive models”Geographical Analysis41158–180.
9.
FotheringhamA SBrunsdonC, 1999, “Local forms of spatial analysis”Geographical Analysis31340–358.
10.
FotheringhamA SBrunsdonCCharltonM, 2002Geographically Weighted Regression: The Analysis of Spatially Varying Relationships (John Wiley, Chichester, Sussex).
11.
GelfandA EKimH JSirmansC FBanerjeeS, 2003, “Spatial modeling with spatially varying coefficient processes”Journal of the American Statistical Association98 (462) 387–396.
12.
GoldbergerA S, 1991A Course in Econometrics (Harvard University Press, Cambridge, MA).
13.
GriffithD A, 2008, “Spatial-filtering-based contributions to a critique of geographically weighted regression (GWR)”Environment and Planning A402751–2769.
14.
HarrisPFotheringhamA SCrespoRCharltonM, 2010, “The use of geographically weighted regression for spatial prediction: An evaluation of models using simulated data sets”Mathematical Geosciences42657–680.
15.
HarrisPBrunsdonCFotheringhamA S, 2011, “Links, comparisons and extensions of the geographically weighted regression model when used as a spatial predictor”Stochastic Environmental Research and Risk Assessment25 (2) 123–138.
16.
JetzWRahbekCLichsteinJ W, 2005, “Local and global approaches to spatial data analysis in ecology”Global Ecology and Biogeography14 (1) 97–98.
17.
LeungYMeiC LZhangW X, 2000, “Statistical tests for spatial nonstationarity based on the geographically weighted regression model”Environment and Planning A329–32.
18.
McMillenD P, 1996, “One hundred fifty years of land values in Chicago: A nonparametric approach”Journal of Urban Economics40100–124.
19.
McMillenD P, 2003, “Spatial autocorrelation or model misspecification?”International Regional Science Review26208–217.
20.
PáezA, 2005, “Local analysis of spatial relationships: A comparison of GWR and the expansion method”Lecture Notes in Computer Science3482162–172.
21.
PáezAWheelerD C, 2009, “Geographically weighted regression”, in International Encyclopedia of Human Geography Eds KitchinRThriftN (Elsevier, Amsterdam).
22.
PáezALongFFarberS, 2008, “Moving window approaches for hedonic price estimation: An empirical comparison of modeling techniques”Urban Studies451565–1581.
23.
PeltoC RElkinsT ABoydH A, 1968, “Automatic contouring of irregularly spaced data”Geophysics33323–343.
24.
WangNMeiC LYanX D, 2008, “Local linear estimation of spatially varying coefficient models: An improvement on the geographically weighted regression technique”Environment and Planning A40986–1005.
25.
WheelerD C, 2007, “Diagnostic tools and a remedial method for collinearity in geographically weighted regression”Environment and Planning A392464–2481.
26.
WheelerD C, 2009, “Simultaneous coefficient penalization and model selection in geographically weighted regression: The geographically weighted lasso”Environment and Planning A41722–742.
27.
WheelerD C, 2010, “Visualizing and diagnosing coefficients from geographically weighted regression”, in Geospatial Analysis and Modeling of Urban Structure and Dynamics Eds JiangBYaoX (Springer, New York) pp 415–436.
28.
WheelerD CCalderC A, 2007, “An assessment of coefficient accuracy in linear regression models with spatially varying coefficients”Journal of Geographical Systems9 (2) 145–166.
29.
WheelerD CPáezA, 2010, “Geographically weighted regression”, in Handbook of Applied Spatial Analysis Eds FischerM MGetisA (Springer, Berlin) pp 461–486.
30.
WheelerDTiefelsdorfM, 2005, “Multicollinearity and correlation among local regression coefficients in geographically weighted regression”Journal of Geographical Systems7 (2) 161–187.
31.
WheelerD CWallerL A, 2009, “Comparing spatially varying coefficient models: A case study examining violent crime rates and their relationships to alcohol outlets and illegal drug arrests”Journal of Geographical Systems11 (1) 1–22.
