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

Author

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  • 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
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    References listed on IDEAS

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    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.
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