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Geographically weighted regression and multicollinearity: dispelling the myth

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  • A. Stewart Fotheringham

    (Arizona State University)

  • Taylor M. Oshan

    (Arizona State University)

Abstract

Geographically weighted regression (GWR) extends the familiar regression framework by estimating a set of parameters for any number of locations within a study area, rather than producing a single parameter estimate for each relationship specified in the model. Recent literature has suggested that GWR is highly susceptible to the effects of multicollinearity between explanatory variables and has proposed a series of local measures of multicollinearity as an indicator of potential problems. In this paper, we employ a controlled simulation to demonstrate that GWR is in fact very robust to the effects of multicollinearity. Consequently, the contention that GWR is highly susceptible to multicollinearity issues needs rethinking.

Suggested Citation

  • A. Stewart Fotheringham & Taylor M. Oshan, 2016. "Geographically weighted regression and multicollinearity: dispelling the myth," Journal of Geographical Systems, Springer, vol. 18(4), pages 303-329, October.
    • Handle: RePEc:kap:jgeosy:v:18:y:2016:i:4:d:10.1007_s10109-016-0239-5
    DOI: 10.1007/s10109-016-0239-5
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    References listed on IDEAS

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    1. David C Wheeler, 2009. "Simultaneous Coefficient Penalization and Model Selection in Geographically Weighted Regression: The Geographically Weighted Lasso," Environment and Planning A, , vol. 41(3), pages 722-742, March.
    2. David Wheeler & Catherine Calder, 2007. "An assessment of coefficient accuracy in linear regression models with spatially varying coefficients," Journal of Geographical Systems, Springer, vol. 9(2), pages 145-166, June.
    3. Antonio Páez & Steven Farber & David Wheeler, 2011. "A Simulation-Based Study of Geographically Weighted Regression as a Method for Investigating Spatially Varying Relationships," Environment and Planning A, , vol. 43(12), pages 2992-3010, December.
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    5. David Wheeler & Lance Waller, 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 Systems, Springer, vol. 11(1), pages 1-22, March.
    6. M. Bárcena & P. Menéndez & M. Palacios & F. Tusell, 2014. "Alleviating the effect of collinearity in geographically weighted regression," Journal of Geographical Systems, Springer, vol. 16(4), pages 441-466, October.
    7. 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.
    8. 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.
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    Cited by:

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    6. Alexis Comber & Paul Harris, 2018. "Geographically weighted elastic net logistic regression," Journal of Geographical Systems, Springer, vol. 20(4), pages 317-341, October.
    7. Li, Mengya & Kwan, Mei-Po & Hu, Wenyan & Li, Rui & Wang, Jun, 2023. "Examining the effects of station-level factors on metro ridership using multiscale geographically weighted regression," Journal of Transport Geography, Elsevier, vol. 113(C).
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    9. Joseph Gibbons, 2021. "Distancing the socially distanced: Racial/ethnic composition’s association with physical distancing in response to COVID-19 in the U.S," PLOS ONE, Public Library of Science, vol. 16(5), pages 1-21, May.
    10. I-Chun Chen & Kuang-Ly Cheng & Hwong-Wen Ma & Cathy C.W. Hung, 2021. "Identifying Spatial Driving Factors of Energy and Water Consumption in the Context of Urban Transformation," Sustainability, MDPI, vol. 13(19), pages 1-18, September.
    11. Oshan, Taylor M. & Smith, Jordan & Fotheringham, Alexander Stewart, 2020. "Targeting the spatial context of obesity determinants via multiscale geographically weighted regression," OSF Preprints u7j29, Center for Open Science.
    12. 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.
    13. Hoehun Ha & Wei Tu, 2018. "An Ecological Study on the Spatially Varying Relationship between County-Level Suicide Rates and Altitude in the United States," IJERPH, MDPI, vol. 15(4), pages 1-16, April.
    14. Obelheiro, Marta Rodrigues & da Silva, Alan Ricardo & Nodari, Christine Tessele & Cybis, Helena Beatriz Bettella & Lindau, Luis Antonio, 2020. "A new zone system to analyze the spatial relationships between the built environment and traffic safety," Journal of Transport Geography, Elsevier, vol. 84(C).
    15. Geniaux, Ghislain & Martinetti, Davide, 2018. "A new method for dealing simultaneously with spatial autocorrelation and spatial heterogeneity in regression models," Regional Science and Urban Economics, Elsevier, vol. 72(C), pages 74-85.
    16. Oshan, Taylor M., 2022. "Navigating the methodological landscape in spatial analysis: a comment on ‘A Route Map for Successful Applications of Geographically-Weighted Regression’," OSF Preprints rckzj, Center for Open Science.
    17. Fei Han & Xinqi Zheng & Peipei Wang & Dongya Liu & Minrui Zheng, 2022. "Effects of Meteorological Factors and Air Pollutants on COVID-19 Transmission under the Action of Control Measures," IJERPH, MDPI, vol. 19(15), pages 1-19, July.
    18. Sisman, S. & Aydinoglu, A.C., 2022. "A modelling approach with geographically weighted regression methods for determining geographic variation and influencing factors in housing price: A case in Istanbul," Land Use Policy, Elsevier, vol. 119(C).
    19. Nana Yang & Jiansong Li & Binbin Lu & Minghai Luo & Linze Li, 2019. "Exploring the Spatial Pattern and Influencing Factors of Land Carrying Capacity in Wuhan," Sustainability, MDPI, vol. 11(10), pages 1-16, May.
    20. Xin Lao & Hengyu Gu, 2020. "Unveiling various spatial patterns of determinants of hukou transfer intentions in China: A multi‐scale geographically weighted regression approach," Growth and Change, Wiley Blackwell, vol. 51(4), pages 1860-1876, December.
    21. Wang, Di & Zhou, Tao & Wang, Mengmeng, 2021. "Information and communication technology (ICT), digital divide and urbanization: Evidence from Chinese cities," Technology in Society, Elsevier, vol. 64(C).
    22. Marta Nalej & Elżbieta Lewandowicz, 2023. "An Analysis of Recreational and Leisure Areas in Polish Counties with the Use of Geographically Weighted Regression," Sustainability, MDPI, vol. 16(1), pages 1-26, December.
    23. Chacon-Hurtado, Davis & Kumar, Indraneel & Gkritza, Konstantina & Fricker, Jon D. & Beaulieu, Lionel J., 2020. "The role of transportation accessibility in regional economic resilience," Journal of Transport Geography, Elsevier, vol. 84(C).

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    More about this item

    Keywords

    Geographically weighted regression; GWR; Collinearity; Regression diagnostics;
    All these keywords.

    JEL classification:

    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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