Journal of Geographical Systems

, Volume 18, Issue 4, pp 303–329 | Cite as

Geographically weighted regression and multicollinearity: dispelling the myth

Original Article

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.

Keywords

Geographically weighted regression GWR Collinearity Regression diagnostics 

JEL Classification

C18 Methodological issues: general C52 Model evaluation, validation, and selection 

Notes

Acknowledgments

We would like to thank two anonymous reviewers and the editor-in-chief for their helpful comments, which improved the quality of this research.

References

  1. Bãrcena MJ, Menãndez P, Palacios MB, Tusell F (2014) Alleviating the effect of collinearity in geographically weighted regression. J Geogr Syst 16(4):441–466. doi: 10.1007/s10109-014-0199-6 CrossRefGoogle Scholar
  2. Belsey DA, Kuh E, Welsch RE (1980) Regression diagnostics: identifying influential data and sources of collinearity. Wiley, New YorkCrossRefGoogle Scholar
  3. Bonferroni CE (1935) Il calcolo delle assicurazioni su gruppi di teste. In: Studi in Onore del Professor Salvatore Ortu Carboni, Rome, pp 13–60Google Scholar
  4. Brown S, Versace VL, Laurenson L, Ierodiaconou D, Fawcett J, Salzman S (2011) Assessment of spatiotemporal varying relationships between rainfall, land cover and surface water area using geographically weighted regression. Environ Model Assess 17(3):241–254. doi: 10.1007/s10666-011-9289-8. http://link.springer.com.ezproxy1.lib.asu.edu/article/10.1007/s10666-011-9289-8
  5. Brunsdon C, Charlton M, Harris P (2012) Living with collinearity in local regression models. http://eprints.maynoothuniversity.ie/5755/
  6. Byrne G, Charlton M, Fotheringham S (2009) Multiple dependent hypothesis tests in geographically weighted regression. In: Lees BG, Laffan SW (eds) Proceedings of the 10th international conference on geocomputation, University of New South Wales. http://eprints.maynoothuniversity.ie/5768/
  7. Cahill M, Mulligan G (2007) Using geographically weighted regression to explore local crime patterns. Soc Sci Comput Rev 25(2):174–193. doi: 10.1177/0894439307298925. http://ssc.sagepub.com.ezproxy1.lib.asu.edu/content/25/2/174
  8. da Silva AR, Fotheringham AS (2015) The multiple testing issue in geographically weighted regression: the multiple testing issue in gwr. Geogr Anal. doi: 10.1111/gean.12084 Google Scholar
  9. Finley AO (2011) Comparing spatially-varying coefficients models for analysis of ecological data with non-stationary and anisotropic residual dependence: spatially-varying coefficients models. Methods Ecol Evol 2(2):143–154. doi: 10.1111/j.2041-210X.2010.00060.x CrossRefGoogle Scholar
  10. Fotheringham AS (1982) Multicollinearity and parameter estimates in a linear model. Geogr Anal 14(1):64–71. doi: 10.1111/j.1538-4632.1982.tb00055.x. http://onlinelibrary.wiley.com/doi/10.1111/j.1538-4632.1982.tb00055.x/abstract
  11. Fotheringham AS, Brunsdon C (1999) Local forms of spatial analysis. Geogr Anal 31(4):340–358. doi: 10.1111/j.1538-4632.1999.tb00989.x. http://onlinelibrary.wiley.com/doi/10.1111/j.1538-4632.1999.tb00989.x/abstract
  12. Fotheringham AS, Brunsdon C, Charlton M (2002) Geographically weighted regression: the analysis of spatially varying relationships. Wiley, New YorkGoogle Scholar
  13. Fotheringham AS, Crespo R, Yao J (2015) Geographical and temporal weighted regression (GTWR). Geogr Anal 47(4):431–452. doi: 10.1111/gean.12071. http://onlinelibrary.wiley.com/doi/10.1111/gean.12071/abstract
  14. Gilbert A, Chakraborty J (2011) Using geographically weighted regression for environmental justice analysis: cumulative cancer risks from air toxics in Florida. Soc Sci Res 40(1):273–286. doi: 10.1016/j.ssresearch.2010.08.006. http://www.sciencedirect.com/science/article/pii/S0049089X10001754
  15. Miller JA, Hanham RQ (2011) Spatial nonstationarity and the scale of species environment relationships in the Mojave Desert, California. USA. Int J Geogr Inf Sci 25(3):423–438. doi: 10.1080/13658816.2010.518147 CrossRefGoogle Scholar
  16. Montgomery DC, Peck EA, Vining GG (2012) Introduction to linear regression analysis, 5th edn. Wiley, New JerseyGoogle Scholar
  17. O’Brien RM (2007) A caution regarding rules of thumb for variance inflation factors. Qual Quant 41(5):673–690. doi: 10.1007/s11135-006-9018-6 CrossRefGoogle Scholar
  18. Páez A, Farber S, Wheeler D (2011) A simulation-based study of geographically weighted regression as a method for investigating spatially varying relationships. Environ Plan A 43(12):2992–3010. doi:10.1068/a44111. http://epn.sagepub.com/content/43/12/2992
  19. Waller LA, Zhu L, Gotway CA, Gorman DM, Gruenewald PJ (2007) Quantifying geographic variations in associations between alcohol distribution and violence: a comparison of geographically weighted regression and spatially varying coefficient models. Stoch Environ Res Risk Assess 21(5):573–588. doi: 10.1007/s00477-007-0139-9 CrossRefGoogle Scholar
  20. Wheeler DC (2007) Diagnostic tools and a remedial method for collinearity in geographically weighted regression. Environ Plan A 39(10):2464–2481. doi: 10.1068/a38325. http://epn.sagepub.com/content/39/10/2464
  21. Wheeler DC (2009) Simultaneous coefficient penalization and model selection in geographically weighted regression: the geographically weighted lasso. Environ Plan A 41(3):722–742. doi: 10.1068/a40256. http://epn.sagepub.com/content/41/3/722
  22. Wheeler DC (2010) Visualizing and diagnosing coefficients from geographically weighted regression models. In: Jiang B, Yao X (eds) Geospatial analysis and modelling of urban structure and dynamics, vol 99. Springer, Dordrecht, pp 415–436. http://link.springer.com/10.1007/978-90-481-8572-621
  23. Wheeler DC, Calder CA (2007) An assessment of coefficient accuracy in linear regression models with spatially varying coefficients. J Geogr Syst 9(2):145–166. doi: 10.1007/s10109-006-0040-y CrossRefGoogle Scholar
  24. Wheeler D, Tiefelsdorf M (2005) Multicollinearity and correlation among local regression coefficients in geographically weighted regression. J Geogr Syst 7(2):161–187. doi: 10.1007/s10109-005-0155-6 CrossRefGoogle Scholar
  25. Wheeler DC, Waller LA (2009) Comparing spatially varying coefficient models: a case study examining violent crime rates and their relationships to alcohol outlets and illegal drug arrests. J Geogr Syst 11(1):1–22. doi: 10.1007/s10109-008-0073-5. http://search.proquest.com.ezproxy1.lib.asu.edu/docview/230073360/abstract
  26. Williams VSL, Jones LV, Tukey JW (1999) Controlling error in multiple comparisons, with examples from state-to-state differences in educational achievement. J Educ Behav Stat 24(1):42–69CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.School of Geographical Sciences and Urban Planning, Arizona State University Coor HallArizona State UniversityTempeUSA

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