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

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  • 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
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    References listed on IDEAS

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    1. 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.
    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. 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.
    4. 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.
    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.
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    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.

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