IDEAS home Printed from https://ideas.repec.org/a/sae/envira/v39y2007i10p2464-2481.html
   My bibliography  Save this article

Diagnostic Tools and a Remedial Method for Collinearity in Geographically Weighted Regression

Author

Listed:
  • David C Wheeler

    (Department of Biostatistics, Emory University, Atlanta, GA 30322, USA)

Abstract

Geographically weighted regression (GWR) is drawing attention as a statistical method to estimate regression models with spatially varying relationships between explanatory variables and a response variable. Local collinearity in weighted explanatory variables leads to GWR coefficient estimates that are correlated locally and across space, have inflated variances, and are at times counterintuitive and contradictory in sign to the global regression estimates. The presence of local collinearity in the absence of global collinearity necessitates the use of diagnostic tools in the local regression model building process to highlight areas in which the results are not reliable for statistical inference. The method of ridge regression can also be integrated into the GWR framework to constrain and stabilize regression coefficients and lower prediction error. This paper presents numerous diagnostic tools and ridge regression in GWR and demonstrates the utility of these techniques with an example using the Columbus crime dataset.

Suggested Citation

  • 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.
    • Handle: RePEc:sae:envira:v:39:y:2007:i:10:p:2464-2481
    DOI: 10.1068/a38325
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.1068/a38325
    Download Restriction: no
    File URL: https://libkey.io/10.1068/a38325?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
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    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. 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.
    2. Yaxiong Ma & Sucharita Gopal, 2018. "Geographically Weighted Regression Models in Estimating Median Home Prices in Towns of Massachusetts Based on an Urban Sustainability Framework," Sustainability, MDPI, vol. 10(4), pages 1-27, March.
    3. 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.
    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. Bauweraerts, Jonathan & Colot, Olivier, 2017. "Exploring nonlinear effects of family involvement in the board on entrepreneurial orientation," Journal of Business Research, Elsevier, vol. 70(C), pages 185-192.
    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. 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.
    8. Bauweraerts, Jonathan & Sciascia, Salvatore & Naldi, Lucia & Mazzola, Pietro, 2019. "Family CEO and board service: Turning the tide for export scope in family SMEs," International Business Review, Elsevier, vol. 28(5), pages 1-1.
    9. Jinjun Tang & Fan Gao & Fang Liu & Wenhui Zhang & Yong Qi, 2019. "Understanding Spatio-Temporal Characteristics of Urban Travel Demand Based on the Combination of GWR and GLM," Sustainability, MDPI, vol. 11(19), pages 1-19, October.
    10. Alexis Comber & Paul Harris, 2018. "Geographically weighted elastic net logistic regression," Journal of Geographical Systems, Springer, vol. 20(4), pages 317-341, October.
    11. 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.
    12. Daria Ciriaci & Daniela Palma, 2008. "The role of knowledge‐based supply specialisation for competitiveness: A spatial econometric approach," Papers in Regional Science, Wiley Blackwell, vol. 87(3), pages 453-475, August.
    13. Yonghua Zou, 2015. "Re-examining the Neighborhood Distribution of Higher Priced Mortgage Lending: Global versus Local Methods," Growth and Change, Wiley Blackwell, vol. 46(4), pages 654-674, December.
    14. Bo Pieter Johannes Andree & Francisco Blasques & Eric Koomen, 2017. "Smooth Transition Spatial Autoregressive Models," Tinbergen Institute Discussion Papers 17-050/III, Tinbergen Institute.

    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. 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.
    3. Jiao, Xiaoying & Li, Gang & Chen, Jason Li, 2020. "Forecasting international tourism demand: a local spatiotemporal model," Annals of Tourism Research, Elsevier, vol. 83(C).
    4. Rojas, Carolina & Páez, Antonio & Barbosa, Olga & Carrasco, Juan, 2016. "Accessibility to urban green spaces in Chilean cities using adaptive thresholds," Journal of Transport Geography, Elsevier, vol. 57(C), pages 227-240.
    5. Daisuke Murakami & Morito Tsutsumi, 2015. "Area-to-point parameter estimation with geographically weighted regression," Journal of Geographical Systems, Springer, vol. 17(3), pages 207-225, July.
    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. 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.
    8. 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.
    9. Chih-Hao Wang & Na Chen, 2021. "A multi-objective optimization approach to balancing economic efficiency and equity in accessibility to multi-use paths," Transportation, Springer, vol. 48(4), pages 1967-1986, August.
    10. Oshan, Taylor M. & Kang, Wei, 2024. "Scale and Correlation in Multiscale Geographically Weighted Regression (MGWR)," OSF Preprints cujby, Center for Open Science.
    11. Tsimpanos, Apostolos & Tsimbos, Cleon & Kalogirou, Stamatis, 2018. "Assessing spatial variation and heterogeneity of fertility in Greece at local authority level," MPRA Paper 100406, University Library of Munich, Germany.
    12. Diana Gutiérrez Posada & Fernando Rubiera Morollón & Ana Viñuela, 2018. "Ageing Places in an Ageing Country: The Local Dynamics of the Elderly Population in Spain," Tijdschrift voor Economische en Sociale Geografie, Royal Dutch Geographical Society KNAG, vol. 109(3), pages 332-349, July.
    13. 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.
    14. Román Mínguez & Roberto Basile & María Durbán, 2024. "Pspatreg: R Package for Semiparametric Spatial Autoregressive Models," Mathematics, MDPI, vol. 12(22), pages 1-27, November.
    15. Daniel Acheampong & Tanya Benford, 2020. "Alternative Treatment Of Contribution In Aid Of Construction: The Impact On Investor-Owned Utility Plant Asset Replacement," Accounting & Taxation, The Institute for Business and Finance Research, vol. 12(1), pages 81-96.
    16. Yu, Haitao & Peng, Zhong-Ren, 2019. "Exploring the spatial variation of ridesourcing demand and its relationship to built environment and socioeconomic factors with the geographically weighted Poisson regression," Journal of Transport Geography, Elsevier, vol. 75(C), pages 147-163.
    17. Kristoffer B. Birkeland & Allan D. D'Silva & Roland Füss & Are Oust, 2021. "The Predictability of House Prices: "Human Against Machine"," International Real Estate Review, Global Social Science Institute, vol. 24(2), pages 139-183.
    18. Abdullah Al Saim & Mohamed H. Aly, 2022. "Machine Learning for Modeling Wildfire Susceptibility at the State Level: An Example from Arkansas, USA," Geographies, MDPI, vol. 2(1), pages 1-17, January.
    19. 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.
    20. Alexis Comber & Paul Harris, 2018. "Geographically weighted elastic net logistic regression," Journal of Geographical Systems, Springer, vol. 20(4), pages 317-341, October.

    More about this item

    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:sae:envira:v:39:y:2007:i:10:p:2464-2481. 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: SAGE Publications (email available below). General contact details of provider: .

    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.