Spatial autocorrelation approaches to testing residuals from least squares regression

TL;DR

This paper introduces two novel spatial autocorrelation-based statistics to test residual serial correlation in regression analysis, especially effective for spatial cross-sectional data where traditional methods like Durbin-Watson fail.

Contribution

The paper develops new spatial autocorrelation statistics for residual analysis, overcoming limitations of the Durbin-Watson test in spatial cross-sectional data.

Findings

New statistics effectively detect residual serial correlation in spatial data.

Application to China's regional data demonstrates practical utility.

The methods complement and improve upon traditional tests.

Abstract

In statistics, the Durbin-Watson test is always employed to detect the presence of serial correlation of residuals from a least squares regression analysis. 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 Durbin-Watson will be ineffectual because the value of Durbin-Watson's statistic depends on the sequences of data point arrangement. Based on the ideas from spatial autocorrelation, this paper presents 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 on the analogy of the Durbin-Watson statistic, a serial correlation index is constructed. As a case, the two statistics are applied to the spatial sample of 29 China's regions. These results show that the new spatial autocorrelation model can be used to test the serial correlation of residuals from regression analysis. In practice, the new statistics can make up for the deficiency of the Durbin-Watson test.