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Diagnostic Tools and a Remedial Method for Collinearity in Geographically Weighted Regression

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  • David C Wheeler

    (Department of Biostatistics, Emory University, Atlanta, GA 30322, USA)

Abstract

Geographically weighted regression (GWR) is drawing attention as a statistical method to estimate regression models with spatially varying relationships between explanatory variables and a response variable. Local collinearity in weighted explanatory variables leads to GWR coefficient estimates that are correlated locally and across space, have inflated variances, and are at times counterintuitive and contradictory in sign to the global regression estimates. The presence of local collinearity in the absence of global collinearity necessitates the use of diagnostic tools in the local regression model building process to highlight areas in which the results are not reliable for statistical inference. The method of ridge regression can also be integrated into the GWR framework to constrain and stabilize regression coefficients and lower prediction error. This paper presents numerous diagnostic tools and ridge regression in GWR and demonstrates the utility of these techniques with an example using the Columbus crime dataset.

Suggested Citation

  • David C Wheeler, 2007. "Diagnostic Tools and a Remedial Method for Collinearity in Geographically Weighted Regression," Environment and Planning A, , vol. 39(10), pages 2464-2481, October.
    • Handle: RePEc:sae:envira:v:39:y:2007:i:10:p:2464-2481
    DOI: 10.1068/a38325
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    References listed on IDEAS

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    1. Antonio Páez & Takashi Uchida & Kazuaki Miyamoto, 2002. "A General Framework for Estimation and Inference of Geographically Weighted Regression Models: 1. Location-Specific Kernel Bandwidths and a Test for Locational Heterogeneity," Environment and Planning A, , vol. 34(4), pages 733-754, April.
    2. David Wheeler & Michael Tiefelsdorf, 2005. "Multicollinearity and correlation among local regression coefficients in geographically weighted regression," Journal of Geographical Systems, Springer, vol. 7(2), pages 161-187, June.
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    2. Yaxiong Ma & Sucharita Gopal, 2018. "Geographically Weighted Regression Models in Estimating Median Home Prices in Towns of Massachusetts Based on an Urban Sustainability Framework," Sustainability, MDPI, vol. 10(4), pages 1-27, March.
    3. Christos Agiakloglou & Cleon Tsimbos & Apostolos Tsimpanos, 2019. "Evidence of spurious results along with spatially autocorrelated errors in the context of geographically weighted regression for two independent SAR(1) processes," Empirical Economics, Springer, vol. 57(5), pages 1613-1631, November.
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    7. Wenjie Wu & Guanpeng Dong & Wenzhong Zhang, 2017. "The puzzling heterogeneity of amenity capitalization effects on land markets," Papers in Regional Science, Wiley Blackwell, vol. 96, pages 135-153, March.
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    10. Alexis Comber & Paul Harris, 2018. "Geographically weighted elastic net logistic regression," Journal of Geographical Systems, Springer, vol. 20(4), pages 317-341, October.
    11. Löchl, Michael & Axhausen, Kay W., 2010. "Modelling hedonic residential rents for land use and transport simulation while considering spatial effects," The Journal of Transport and Land Use, Center for Transportation Studies, University of Minnesota, vol. 3(2), pages 39-63.
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    14. Bo Pieter Johannes Andree & Francisco Blasques & Eric Koomen, 2017. "Smooth Transition Spatial Autoregressive Models," Tinbergen Institute Discussion Papers 17-050/III, Tinbergen Institute.

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