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Spatial Autocorrelation Approaches to Testing Residuals from Least Squares Regression

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  • Yanguang Chen

Abstract

In geo-statistics, the Durbin-Watson test is frequently employed to detect the presence of residual serial correlation from least squares regression analyses. However, the Durbin-Watson statistic is only suitable for ordered time or spatial series. If the variables comprise cross-sectional data coming from spatial random sampling, the test will be ineffectual because the value of Durbin-Watson’s statistic depends on the sequence of data points. This paper develops two new statistics for testing serial correlation of residuals from least squares regression based on spatial samples. By analogy with the new form of Moran’s index, an autocorrelation coefficient is defined with a standardized residual vector and a normalized spatial weight matrix. Then by analogy with the Durbin-Watson statistic, two types of new serial correlation indices are constructed. As a case study, the two newly presented statistics are applied to a spatial sample of 29 China’s regions. These results show that the new spatial autocorrelation models can be used to test the serial correlation of residuals from regression analysis. In practice, the new statistics can make up for the deficiencies of the Durbin-Watson test.

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  • Yanguang Chen, 2016. "Spatial Autocorrelation Approaches to Testing Residuals from Least Squares Regression," PLOS ONE, Public Library of Science, vol. 11(1), pages 1-19, January.
    • Handle: RePEc:plo:pone00:0146865
    DOI: 10.1371/journal.pone.0146865
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    References listed on IDEAS

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    1. Yanguang Chen, 2015. "A New Methodology of Spatial Cross-Correlation Analysis," PLOS ONE, Public Library of Science, vol. 10(5), pages 1-20, May.
    2. Yanguang Chen, 2012. "On the four types of weight functions for spatial contiguity matrix," Letters in Spatial and Resource Sciences, Springer, vol. 5(2), pages 65-72, July.
    3. Sargan, John Denis & Bhargava, Alok, 1983. "Testing Residuals from Least Squares Regression for Being Generated by the Gaussian Random Walk," Econometrica, Econometric Society, vol. 51(1), pages 153-174, January.
    4. Yanguang Chen, 2013. "New Approaches for Calculating Moran’s Index of Spatial Autocorrelation," PLOS ONE, Public Library of Science, vol. 8(7), pages 1-14, July.
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