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Alleviating the effect of collinearity in geographically weighted regression

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  • M. Bárcena
  • P. Menéndez
  • M. Palacios
  • F. Tusell

Abstract

Geographically weighted regression (GWR) is a popular technique to deal with spatially varying relationships between a response variable and predictors. Problems, however, have been pointed out (see Wheeler and Tiefelsdorf in J Geogr Syst 7(2):161–187, 2005 ), which appear to be related to locally poor designs, with severe impact on the estimation of coefficients. Different remedies have been proposed. We propose two regularization methods. The first one is generalized ridge regression, which can also be seen as an empirical Bayes method. We show that it can be implemented using ordinary GWR software with an appropriate choice of the weights. The second one augments the local sample as needed while running GWR. We illustrate both methods along with ordinary GWR on an example of housing prices in the city of Bilbao (Spain) and using simulations. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • 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.
    • Handle: RePEc:kap:jgeosy:v:16:y:2014:i:4:p:441-466
    DOI: 10.1007/s10109-014-0199-6
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    1. repec:ehu:biltok:5463 is not listed on IDEAS
    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. Diego Vidaurre & Concha Bielza & Pedro Larrañaga, 2012. "Lazy lasso for local regression," Computational Statistics, Springer, vol. 27(3), pages 531-550, September.
    4. 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.
    5. Steven Farber & Antonio Páez, 2007. "A systematic investigation of cross-validation in GWR model estimation: empirical analysis and Monte Carlo simulations," Journal of Geographical Systems, Springer, vol. 9(4), pages 371-396, December.
    6. 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.
    7. Christopher Bitter & Gordon Mulligan & Sandy Dall’erba, 2007. "Incorporating spatial variation in housing attribute prices: a comparison of geographically weighted regression and the spatial expansion method," Journal of Geographical Systems, Springer, vol. 9(1), pages 7-27, April.
    8. Gelfand A.E. & Kim H-J. & Sirmans C.F. & Banerjee S., 2003. "Spatial Modeling With Spatially Varying Coefficient Processes," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 387-396, January.
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    1. Dongwoo Kang & Sandy Dall’erba, 2016. "Exploring the spatially varying innovation capacity of the US counties in the framework of Griliches’ knowledge production function: a mixed GWR approach," Journal of Geographical Systems, Springer, vol. 18(2), pages 125-157, April.
    2. Mulley, Corinne & Ma, Liang & Clifton, Geoffrey & Yen, Barbara & Burke, Matthew, 2016. "Residential property value impacts of proximity to transport infrastructure: An investigation of bus rapid transit and heavy rail networks in Brisbane, Australia," Journal of Transport Geography, Elsevier, vol. 54(C), pages 41-52.
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    5. Paliska, Dejan & Drobne, Samo, 2020. "Impact of new motorway on housing prices in rural North-East Slovenia," Journal of Transport Geography, Elsevier, vol. 88(C).
    6. 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.
    7. Qianyao Li & Junwu Wang & Judith Callanan & Binbin Lu & Zeng Guo, 2021. "The spatial varying relationship between services of the train network and residential property values in Melbourne, Australia," Urban Studies, Urban Studies Journal Limited, vol. 58(2), pages 335-354, February.
    8. Alexis Comber & Khanh Chi & Man Q Huy & Quan Nguyen & Binbin Lu & Hoang H Phe & Paul Harris, 2020. "Distance metric choice can both reduce and induce collinearity in geographically weighted regression," Environment and Planning B, , vol. 47(3), pages 489-507, March.
    9. 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.

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    More about this item

    Keywords

    Geographically weighted regression; GWR; Shrinkage estimators; Spatial models; C13 Estimation; C14 Semiparametric and non parametric methods; C63 Computational techniques;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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