IDEAS home Printed from https://ideas.repec.org/a/sae/envira/v43y2011i7p1723-1745.html
   My bibliography  Save this article

Spatially Varying Coefficient Models: Testing for Spatial Heteroscedasticity and Reweighting Estimation of the Coefficients

Author

Listed:
  • Si-Lian Shen
  • Chang-Lin Mei
  • Ying-Jian Zhang

Abstract

In the framework of the geographically weighted regression technique, spatial homoscedasticity of the model error term is a common assumption when a spatially varying coefficient model is calibrated to explore spatial nonstationarity of the regression relationship. In many real-world problems, however, this assumption cannot be guaranteed. In this study we first present a residual-based test method for detecting spatial heteroscedasticity of a spatially varying coefficient model. Then, we suggest a local linear smoothing procedure to estimate the variance function of the model error when heteroscedasticity exists, on which a reweighting estimation of the regression coefficients is derived. Some numerical experiments are conducted to evaluate the performance of the test and the gain in accuracy of the coefficient estimates by using the reweighting estimation method. The results demonstrate that the test method is powerful and that the reweighting estimation can improve the accuracy of the coefficient estimates, especially when strong heteroscedasticity exists in the model error term. Finally, a real-world dataset is analyzed to demonstrate the applications of the proposed test and estimation methods.

Suggested Citation

  • Si-Lian Shen & Chang-Lin Mei & Ying-Jian Zhang, 2011. "Spatially Varying Coefficient Models: Testing for Spatial Heteroscedasticity and Reweighting Estimation of the Coefficients," Environment and Planning A, , vol. 43(7), pages 1723-1745, July.
    • Handle: RePEc:sae:envira:v:43:y:2011:i:7:p:1723-1745
    DOI: 10.1068/a43201
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.1068/a43201
    Download Restriction: no
    File URL: https://libkey.io/10.1068/a43201?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. Yee Leung & Chang-Lin Mei & Wen-Xiu Zhang, 2000. "Testing for Spatial Autocorrelation among the Residuals of the Geographically Weighted Regression," Environment and Planning A, , vol. 32(5), pages 871-890, May.
    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. 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.
    4. Yee Leung & Chang-Lin Mei & Wen-Xiu Zhang, 2000. "Statistical Tests for Spatial Nonstationarity Based on the Geographically Weighted Regression Model," Environment and Planning A, , vol. 32(1), pages 9-32, January.
    5. Cleveland, William S. & Devlin, Susan J. & Grosse, Eric, 1988. "Regression by local fitting : Methods, properties, and computational algorithms," Journal of Econometrics, Elsevier, vol. 37(1), pages 87-114, 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. Hongjie Wei & Yan Sun, 2017. "Heteroskedasticity-robust semi-parametric GMM estimation of a spatial model with space-varying coefficients," Spatial Economic Analysis, Taylor & Francis Journals, vol. 12(1), pages 113-128, January.

    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. 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.
    2. repec:rre:publsh:v:51:y:2021:i:2 is not listed on IDEAS
    3. 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.
    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. 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.
    6. 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).
    7. 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.
    8. Wei, Chuan-Hua & Qi, Fei, 2012. "On the estimation and testing of mixed geographically weighted regression models," Economic Modelling, Elsevier, vol. 29(6), pages 2615-2620.
    9. Julie Le Gallo, 2000. "Spatial econometrics (2, Spatial heterogeneity) [Econométrie spatiale (2, Hétérogénéité spatiale)]," Working Papers hal-01526969, HAL.
    10. Yee Leung & Chang-Lin Mei & Wen-Xiu Zhang, 2000. "Testing for Spatial Autocorrelation among the Residuals of the Geographically Weighted Regression," Environment and Planning A, , vol. 32(5), pages 871-890, May.
    11. Ning Wang & Chang-Lin Mei & Xiao-Dong Yan, 2008. "Local Linear Estimation of Spatially Varying Coefficient Models: An Improvement on the Geographically Weighted Regression Technique," Environment and Planning A, , vol. 40(4), pages 986-1005, April.
    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. 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.
    15. 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.
    16. Bell, David & Kay, Jim & Malley, Jim, 1996. "A non-parametric approach to non-linear causality testing," Economics Letters, Elsevier, vol. 51(1), pages 7-18, April.
    17. Sunak, Yasin & Madlener, Reinhard, 2012. "The Impact of Wind Farms on Property Values: A Geographically Weighted Hedonic Pricing Model," FCN Working Papers 3/2012, E.ON Energy Research Center, Future Energy Consumer Needs and Behavior (FCN), revised Mar 2013.
    18. Sumit Agarwal & Ying Fan & Daniel P. McMillen & Tien Foo Sing, 2021. "Tracking the pulse of a city—3D real estate price heat maps," Journal of Regional Science, Wiley Blackwell, vol. 61(3), pages 543-569, June.
    19. Anil Kumar, 2012. "Nonparametric estimation of the impact of taxes on female labor supply," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(3), pages 415-439, April.
    20. John T. Barkoulas & Christopher F. Baum & Joseph Onochie, 1997. "A nonparametric investigation of the 90‐day t‐bill rate," Review of Financial Economics, John Wiley & Sons, vol. 6(2), pages 187-198.
    21. Gary Gorton & Frank Schmid, 2000. "Class Struggle Inside the Firm: A Study of German Codetermination," NBER Working Papers 7945, National Bureau of Economic Research, Inc.

    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:43:y:2011:i:7:p:1723-1745. 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.