Interaction terms are constructed with georeferenced attribute variables and spatial filter eigenvectors, and then used to compute geographically varying regression coefficients. These coefficients, which are analogous to geographically weighted regression (GWR) coefficients, display preferable properties, and this specification is used to critique selected features of GWR. Comparisons are illustrated with the Georgia data appearing in the standard GWR tutorial.
Get full access to this article
View all access options for this article.
References
1.
AlperovichGDeutschJ, 2002, “An application of a switching regimes regression to the study of urban structure”Papers in Regional Science1883–98
2.
AnselinL, 1995, “Local indicators of spatial associations—LISA”Geographical Analysis2793–115
3.
BlumenthalL, 1938Distance Geometries: A Study of the Development of Abstracts Metrics (University of Missouri Press, Columbia, MD)
4.
BorcardDLegendreP, 2002, “All-scale spatial analysis of ecological data by means of principal coordinates of neighbour matrices”Ecological Modelling15351–68
5.
de JongPSprengerCvan VeenF, 1984, “On extreme values of Moran's I and Geary's c”Geographical Analysis1617–24
6.
FotheringhamA SBrunsdonCCharltonM, 2002Geographically Weighted Regression: The Analysis of Spatially Varying Relationships (John Wiley, Chichester, Sussex)
7.
GetisA, 1990, “Screening for spatial dependence in regression analysis”Papers of the Regional Science Association6969–81
8.
GetisA, 1995, “Spatial filtering in a regression framework: Experiments on regional inequality, government expenditures, and urban crime”, in New Directions in Spatial Econometrics Eds AnselinLFloraxR (Springer, New York) pp 172–188
9.
GriffithD, 1979, “Urban dominance, spatial structure and spatial dynamics: Some theoretical conjectures and empirical implications”Economic Geography5595–113
10.
GriffithD, 1981, “Towards a theory of spatial statistics: A rejoinder”Geography Analysis1391–93
11.
GriffithD, 1996, “Spatial autocorrelation and eigenfunctions of the geographic weights matrix accompanying geo-referenced data”Canadian Geographer40351–367
12.
GriffithD, 2000, “A linear regression solution to the spatial autocorrelation problem”Journal of Geographical Systems2141–156
13.
GriffithD, 2003Spatial Autocorrelation and Spatial Filtering: Gaining Understanding Through Theory and Scientific Visualization (Springer, Berlin)
14.
GriffithDFellowsP, 1999, “Pixels and eigenvectors: Classification of LANDSAT TM imagery using spectral and locational information”, in Spatial Accuracy Assessment: Land Information Uncertainty in Natural Resources Eds LowellKJatonA (Ann Arbor Press, Ann Arbor, MI) pp 309–317
15.
GriffithDLagonaF, 1998, “On the quality of likelihood-based estimators in spatial autoregressive models when the data dependence structure is misspecified”Journal of Statistical Planning and Inference69153–174
16.
GriffithDLayneL, 1997, “Uncovering relationships between geo-statistical and spatial autoregressive models”, in the 1996 Proceedings on the Section on Statistics and the EnvironmentAmerican Statistical Association, pp 91–96
17.
GriffithDPeres-NetoP, 2007, “Spatial modeling in ecology: The flexibility of eigenfunction spatial analyses”Ecology872603–2613
18.
HainingR, 1991, “Bivariate correlation and spatial data”Geographical Analysis23210–227
19.
HamsAde RaedtH, 2000, “Fast algorithm for finding the eigenvalue distribution of very large matrices”Physical Review, E: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics624365–4377
20.
JonesJCasettiE (Eds), 1992Applications of the Expansion Method (Routledge, London)
21.
OdenN, 1984, “Assessing the significance of a spatial correlogram”Geographical Analysis161–16
22.
PáezAUchidaTMiyamotoK, 2001, “Spatial association and heterogeneity issues in land price models”Urban Studies381493–1508
23.
PatuelliRGriffithDTiefelsdorfMNijkampP, 2006, “The use of spatial filtering techniques: The spatial and space–time structure of German unemployment data”, DP 06-049/3, Tinbergen Institute, Amsterdam
24.
SpiegelhalterDBestNCarlinBVan der LindeA, 2002, “Bayesian measures of model complexity and fit”Journal of the Royal Statistical Society64B583–640
25.
TiefelsdorfM, 2000Modelling Spatial Processes: The Identification and Analysis of Spatial Relationships in Regression Residuals by Means of Moran's I (Springer, Berlin)
26.
TiefelsdorfM, 2007, “Controlling for migration effects in ecological disease mapping of prostrate cancer”Stochastic Environmental Research and Risk Assessment21615–624
27.
TiefelsdorfMBootsB, 1995, “The exact distribution of Moran's I”Environment and Planning A27985–999
28.
TiefelsdorfMGriffithD, 2007, “Semiparametric filtering of spatial autocorrelation: The eigenvector approach”Environment and Planning A391193–1221
29.
TiefelsdorfMWheelerD, 2004, “Spatial structure effects in regression coefficients of geographically weighted regression”, paper presented to the 51st annual North American meetings of the Regional Science Association International, Seattle, Washington, 12 November
30.
TiefelsdorfMGriffithDBootsB, 1999, “A variance-stabilizing coding scheme for spatial link matrices”Environment and Planning A31165–180
31.
WallerLZhuLGotwayCGormanDGruenewaldP, 2007, “Quantifying geographic variations in associations between alcohol distribution and violence: A comparison of geographically weighted regression and spatially varying coefficient models”Stochastic Environmental Research and Risk Assessment21573–588
32.
WheelerD, 2007, “Diagnostic tools and a remedial method for collinearity in geographically weighted regression”Environment and Planning A392464–2481
33.
WheelerDTiefelsdorfM, 2005, “Multicollinearity and correlation among local regression coefficients in geographically weighted regression”Journal of Geographical Systems7161–187
