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Scale and correlation in multiscale geographically weighted regression (MGWR)

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  • Wei Kang

    (University of California Riverside)

  • Taylor M. Oshan

    (University of Maryland, College Park)

Abstract

Multiscale geographically weighted regression (MGWR) extends geographically weighted regression (GWR) by allowing process heterogeneity to be modeled at different spatial scales. While MGWR improves parameter estimates compared to GWR, the relationship between spatial scale and correlations within and among covariates—specifically spatial autocorrelation and collinearity—has not been systematically explored. This study investigates these relationships through controlled simulation experiments. Results indicate that spatial autocorrelation and collinearity affect specific model components rather than the entire model. Their impacts are cumulative but remain minimal unless they become very strong. MGWR effectively mitigates local multicollinearity issues by applying varying bandwidths across parameter surfaces. However, high levels of spatial autocorrelation and collinearity can lead to bandwidth underestimation for global processes, potentially producing false local effects. Additionally, strong collinearity may cause bandwidths to be overestimated for some processes, which helps mitigate collinearity but may obscure local effects. These findings suggest that while MGWR offers greater robustness against multicollinearity compared to GWR, bandwidth estimates should be interpreted with caution, as they can be influenced by strong spatial autocorrelation and collinearity. These results have important implications for empirical applications of MGWR.

Suggested Citation

  • Wei Kang & Taylor M. Oshan, 2025. "Scale and correlation in multiscale geographically weighted regression (MGWR)," Journal of Geographical Systems, Springer, vol. 27(3), pages 399-424, July.
    • Handle: RePEc:kap:jgeosy:v:27:y:2025:i:3:d:10.1007_s10109-025-00468-1
    DOI: 10.1007/s10109-025-00468-1
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    References listed on IDEAS

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    1. A. Stewart Fotheringham & Ziqi Li & Levi John Wolf, 2021. "Scale, Context, and Heterogeneity: A Spatial Analytical Perspective on the 2016 U.S. Presidential Election," Annals of the American Association of Geographers, Taylor & Francis Journals, vol. 111(6), pages 1602-1621, September.
    2. Ziqi Li & A. Stewart Fotheringham & Taylor M. Oshan & Levi John Wolf, 2020. "Measuring Bandwidth Uncertainty in Multiscale Geographically Weighted Regression Using Akaike Weights," Annals of the American Association of Geographers, Taylor & Francis Journals, vol. 110(5), pages 1500-1520, September.
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    4. 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.
    5. Kenan Li & Nina S. N. Lam, 2018. "Geographically Weighted Elastic Net: A Variable-Selection and Modeling Method under the Spatially Nonstationary Condition," Annals of the American Association of Geographers, Taylor & Francis Journals, vol. 108(6), pages 1582-1600, November.
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    JEL classification:

    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models

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