IDEAS home Printed from https://ideas.repec.org/a/kap/jgeosy/v16y2014i4p441-466.html
   My bibliography  Save this article

Alleviating the effect of collinearity in geographically weighted regression

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10109-014-0199-6
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10109-014-0199-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Maria J. Barcena & Patricia Mendez & Maria B. Palacios & Fernando Tusell, 2013. "Measuring the effect of the real estate bubble: a house price index for Bilbao," Chapters from NBP Conference Publications, in: Hanna Augustyniak & Jacek Łaszek & Krzysztof Olszewski (ed.), Papers presented during the Narodowy Bank Polski Workshop: Recent trends in the real estate market and its analysis, 2013, chapter 15, pages 127-156, Narodowy Bank Polski.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    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. 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.
    3. 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.
    4. 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.
    5. Alexis Comber & Paul Harris, 2018. "Geographically weighted elastic net logistic regression," Journal of Geographical Systems, Springer, vol. 20(4), pages 317-341, October.
    6. 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.
    7. Cankun Wei & Meichen Fu & Li Wang & Hanbing Yang & Feng Tang & Yuqing Xiong, 2022. "The Research Development of Hedonic Price Model-Based Real Estate Appraisal in the Era of Big Data," Land, MDPI, vol. 11(3), pages 1-30, February.
    8. 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).
    9. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. 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.
    3. Marco Helbich & Wolfgang Brunauer & Eric Vaz & Peter Nijkamp, 2014. "Spatial Heterogeneity in Hedonic House Price Models: The Case of Austria," Urban Studies, Urban Studies Journal Limited, vol. 51(2), pages 390-411, February.
    4. 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.
    5. 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.
    6. repec:rre:publsh:v:51:y:2021:i:2 is not listed on IDEAS
    7. Gollini, Isabella & Lu, Binbin & Charlton, Martin & Brunsdon, Christopher & Harris, Paul, 2015. "GWmodel: An R Package for Exploring Spatial Heterogeneity Using Geographically Weighted Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(i17).
    8. Maria Terres & Alan Gelfand, 2015. "Using spatial gradient analysis to clarify species distributions with application to South African protea," Journal of Geographical Systems, Springer, vol. 17(3), pages 227-247, July.
    9. 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.
    10. Anping Chen & Marlon Boarnet & Mark Partridge & Wenjie Wu & Guanpeng Dong, 2014. "Valuing The “Green” Amenities In A Spatial Context," Journal of Regional Science, Wiley Blackwell, vol. 54(4), pages 569-585, September.
    11. 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.
    12. 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.
    13. Cem Ertur & Julie Le Gallo, 2008. "Regional Growth and Convergence: Heterogenous reaction versus interaction in spatial econometric approaches," Working Papers hal-00463274, HAL.
    14. 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.
    15. Wrenn, Douglas H. & Sam, Abdoul G., 2014. "Geographically and temporally weighted likelihood regression: Exploring the spatiotemporal determinants of land use change," Regional Science and Urban Economics, Elsevier, vol. 44(C), pages 60-74.
    16. Redfearn, Christian L., 2009. "How informative are average effects? Hedonic regression and amenity capitalization in complex urban housing markets," Regional Science and Urban Economics, Elsevier, vol. 39(3), pages 297-306, May.
    17. 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.
    18. Mauricio Sarrias, 2020. "Random Parameters and Spatial Heterogeneity using Rchoice in R," REGION, European Regional Science Association, vol. 7, pages 1-19.
    19. Antonio Páez & Fei Long & Steven Farber, 2008. "Moving Window Approaches for Hedonic Price Estimation: An Empirical Comparison of Modelling Techniques," Urban Studies, Urban Studies Journal Limited, vol. 45(8), pages 1565-1581, July.
    20. 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.
    21. Olaru, Doina & Mulley, Corinne & Smith, Brett & Ma, Liang, 2017. "Policy-led selection of the most appropriate empirical model to estimate hedonic prices in the residential market," Journal of Transport Geography, Elsevier, vol. 62(C), pages 213-228.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kap:jgeosy:v:16:y:2014:i:4:p:441-466. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.