Spatial Autocorrelation Approaches to Testing Residuals from Least Squares Regression

Area of Science:

• Geostatistics
• Spatial statistics
• Econometrics

Background:

• The Durbin-Watson test is standard for detecting serial correlation in regression residuals.
• Its applicability is limited to time or spatial series data.
• It is ineffectual for cross-sectional data from spatial random sampling due to data sequence dependency.

Purpose of the Study:

• To develop novel statistics for testing residual serial correlation in spatial samples.
• To address the limitations of the Durbin-Watson test in non-ordered spatial data.
• To provide robust tools for spatial regression analysis.

Main Methods:

• Development of two new statistics analogous to Moran's index and the Durbin-Watson statistic.
• Definition of an autocorrelation coefficient using standardized residuals and a normalized spatial weight matrix.
• Application of the new statistics to a spatial sample of 29 Chinese regions.

Main Results:

• The newly developed spatial autocorrelation models effectively test for serial correlation in regression residuals.
• The proposed statistics demonstrate capability in handling spatial samples.
• Case study results confirm the utility of the new methods.

Conclusions:

• The new spatial statistics offer a viable alternative to the Durbin-Watson test for spatial data.
• These methods enhance the analysis of spatial regression models with cross-sectional data.
• The study provides practical tools to overcome deficiencies in existing serial correlation tests.