IDEAS home Printed from https://ideas.repec.org/a/sae/envira/v34y2002i4p733-754.html
   My bibliography  Save this article

A General Framework for Estimation and Inference of Geographically Weighted Regression Models: 1. Location-Specific Kernel Bandwidths and a Test for Locational Heterogeneity

Author

Listed:
  • Antonio Páez

    (Center for Northeast Asian Studies, Tohoku University, Kawauchi, Aoba-ku, Sendai 980-8576, Japan)

  • Takashi Uchida

    (Graduate School of Engineering, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 9558-8585, Japan)

  • Kazuaki Miyamoto

    (Center for Northeast Asian Studies, Tohoku University, Kawauchi, Aoba-ku, Sendai 980-8576, Japan)

Abstract

Geographically weighted regression (GWR) has been proposed as a technique to explore spatial parametric nonstationarity. The method has been developed mainly along the lines of local regression and smoothing techniques, a strategy that has led to a number of difficult questions about the regularity conditions of the likelihood function, the effective number of degrees of freedom, and in general the relevance of extending the method to derive inference and model specification tests. In this paper we argue that placing GWR within a different statistical context, as a spatial model of error variance heterogeneity, or what might be termed locational heterogeneity, solves these difficulties. A maximum-likelihood-based framework for estimation and inference of a general geographically weighted regression model is presented that leads to a method to estimate location-specific kernel bandwidths. Moreover, a test for locational heterogeneity is derived and its use exemplified with a case study.

Suggested Citation

  • 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.
    • Handle: RePEc:sae:envira:v:34:y:2002:i:4:p:733-754
    DOI: 10.1068/a34110
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.1068/a34110
    Download Restriction: no
    File URL: https://libkey.io/10.1068/a34110?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. Engle, Robert F., 1984. "Wald, likelihood ratio, and Lagrange multiplier tests in econometrics," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 13, pages 775-826, Elsevier.
    2. 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.
    3. Antonio Páez & Takashi Uchida & Kazuaki Miyamoto, 2002. "A General Framework for Estimation and Inference of Geographically Weighted Regression Models: 2. Spatial Association and Model Specification Tests," Environment and Planning A, , vol. 34(5), pages 883-904, May.
    4. T. S. Breusch & A. R. Pagan, 1980. "The Lagrange Multiplier Test and its Applications to Model Specification in Econometrics," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(1), pages 239-253.
    5. Griffith, Daniel A. & Layne, Larry J., 1999. "A Casebook for Spatial Statistical Data Analysis: A Compilation of Different Thematic Data Sets," OUP Catalogue, Oxford University Press, number 9780195109580.
    6. J. Keith Ord & Arthur Getis, 2001. "Testing for Local Spatial Autocorrelation in the Presence of Global Autocorrelation," Journal of Regional Science, Wiley Blackwell, vol. 41(3), pages 411-432, August.
    7. Manfred M. Fischer & Arthur Getis (ed.), 1997. "Recent Developments in Spatial Analysis," Advances in Spatial Science, Springer, number 978-3-662-03499-6.
    Full references (including those not matched with items on IDEAS)

    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. Antonio Páez & Takashi Uchida & Kazuaki Miyamoto, 2002. "A General Framework for Estimation and Inference of Geographically Weighted Regression Models: 2. Spatial Association and Model Specification Tests," Environment and Planning A, , vol. 34(5), pages 883-904, May.
    2. John Geweke & Joel Horowitz & M. Hashem Pesaran, 2006. "Econometrics: A Bird’s Eye View," CESifo Working Paper Series 1870, CESifo.
    3. Yash P. Mehra, 1995. "Some key empirical determinants of short-term nominal interest rates," Economic Quarterly, Federal Reserve Bank of Richmond, issue Sum, pages 33-51.
    4. Adrian C. Darnell, 1994. "A Dictionary Of Econometrics," Books, Edward Elgar Publishing, number 118.
    5. Baltagi, Badi H. & Li, Qi, 1995. "Testing AR(1) against MA(1) disturbances in an error component model," Journal of Econometrics, Elsevier, vol. 68(1), pages 133-151, July.
    6. Sven Müller, 2012. "Identifying spatial nonstationarity in German regional firm start-up data," Review of Regional Research: Jahrbuch für Regionalwissenschaft, Springer;Gesellschaft für Regionalforschung (GfR), vol. 32(2), pages 113-132, September.
    7. 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.
    8. Sang-Il Lee, 2004. "A Generalized Significance Testing Method for Global Measures of Spatial Association: An Extension of the Mantel Test," Environment and Planning A, , vol. 36(9), pages 1687-1703, September.
    9. Gabriele Fiorentini & Enrique Sentana, 2012. "Tests for Serial Dependence in Static, Non-Gaussian Factor Models," Working Papers wp2012_1211, CEMFI.
    10. Eboli, Laura & Forciniti, Carmen & Mazzulla, Gabriella, 2018. "Spatial variation of the perceived transit service quality at rail stations," Transportation Research Part A: Policy and Practice, Elsevier, vol. 114(PA), pages 67-83.
    11. Li, Deng-Kui & Mei, Chang-Lin & Wang, Ning, 2019. "Tests for spatial dependence and heterogeneity in spatially autoregressive varying coefficient models with application to Boston house price analysis," Regional Science and Urban Economics, Elsevier, vol. 79(C).
    12. Miryam S. Merk & Philipp Otto, 2022. "Estimation of the spatial weighting matrix for regular lattice data—An adaptive lasso approach with cross‐sectional resampling," Environmetrics, John Wiley & Sons, Ltd., vol. 33(1), February.
    13. Gabriele Fiorentini & Enrique Sentana, 2019. "Dynamic specification tests for dynamic factor models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(3), pages 325-346, April.
    14. Gabriele Fiorentini & Enrique Sentana, 2009. "Dynamic Specification Tests for Static Factor Models," Working Papers wp2009_0912, CEMFI.
    15. Yock Y. Chong & David F. Hendry, 1986. "Econometric Evaluation of Linear Macro-Economic Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(4), pages 671-690.
    16. King, Maxwell L. & Zhang, Xibin & Akram, Muhammad, 2020. "Hypothesis testing based on a vector of statistics," Journal of Econometrics, Elsevier, vol. 219(2), pages 425-455.
    17. Hamilton, James D., 1996. "Specification testing in Markov-switching time-series models," Journal of Econometrics, Elsevier, vol. 70(1), pages 127-157, January.
    18. Jinyong Hahn & Ruoyao Shi, 2021. "Breusch and Pagan’s (1980) Test Revisited," Working Papers 202110, University of California at Riverside, Department of Economics.
    19. Wooldridge, Jeffrey M., 1991. "On the application of robust, regression- based diagnostics to models of conditional means and conditional variances," Journal of Econometrics, Elsevier, vol. 47(1), pages 5-46, January.
    20. Basu, Ayanendranath & Chakraborty, Soumya & Ghosh, Abhik & Pardo, Leandro, 2022. "Robust density power divergence based tests in multivariate analysis: A comparative overview of different approaches," Journal of Multivariate Analysis, Elsevier, vol. 188(C).

    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:34:y:2002:i:4:p:733-754. 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.