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Local Linear Estimation of Spatially Varying Coefficient Models: An Improvement on the Geographically Weighted Regression Technique

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  • Ning Wang
  • Chang-Lin Mei
  • Xiao-Dong Yan

    (Key Laboratory of Regional Climate-Environment Research for Temperate East Asia, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, People's Republic of China)

Abstract

Geographically weighted regression (GWR), as a useful method for exploring spatial non-stationarity of a regression relationship, has been applied to a variety of areas. In this method a spatially varying coefficient model is locally calibrated and the spatial-variation patterns of the locally estimated regression coefficients are taken as the main evidence of spatial nonstationarity for the underlying data-generating processes. Therefore, the validity of the analysis results drawn by GWR is closely dependent on the accuracy between the underlying coefficients and their estimates. Motivated by the local polynomial-modelling technique in statistics, we propose a local linear-based GWR for the spatially varying coefficient models, in which the coefficients are locally expanded as linear functions of the spatial coordinates and then estimated by the weighted least-squares procedure. Some theoretical and numerical comparisons with GWR are conducted and the results demonstrate that the proposed method can significantly improve GWR, not only in goodness-of-fit of the whole regression function but also in reducing bias of the coefficient estimates.

Suggested Citation

  • 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.
  • Handle: RePEc:sae:envira:v:40:y:2008:i:4:p:986-1005
    DOI: 10.1068/a3941
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Yefang Huang & Yee Leung, 2002. "Analysing regional industrialisation in Jiangsu province using geographically weighted regression," Journal of Geographical Systems, Springer, vol. 4(2), pages 233-249, June.
    4. A. Stewart Fotheringham & Martin Charlton & Chris Brunsdon, 1997. "Measuring Spatial Variations in Relationships with Geographically Weighted Regression," Advances in Spatial Science, in: Manfred M. Fischer & Arthur Getis (ed.), Recent Developments in Spatial Analysis, chapter 4, pages 60-82, Springer.
    5. Ernesto Calvo & Marcelo Escolar, 2003. "The Local Voter: A Geographically Weighted Approach to Ecological Inference," American Journal of Political Science, John Wiley & Sons, vol. 47(1), pages 189-204, January.
    6. 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.
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    Cited by:

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    3. 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.

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