Dataset Information

Spatial Autocorrelation Approaches to Testing Residuals from Least Squares Regression.

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.

SUBMITTER: Chen Y

PROVIDER: S-EPMC4723244 | biostudies-literature | 2016

REPOSITORIES: biostudies-literature

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Publications

Spatial Autocorrelation Approaches to Testing Residuals from Least Squares Regression.

Chen Yanguang Y

PloS one 20160122 1

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 ...[more]

PMID: 26800271

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Project description:Land-use regression (LUR) models have been developed to estimate spatial distributions of traffic-related pollutants. Several studies have examined spatial autocorrelation among residuals in LUR models, but few utilized spatial residual information in model prediction, or examined the impact of modeling methods, monitoring site selection, or traffic data quality on LUR performance. This study aims to improve spatial models for traffic-related pollutants using generalized additive models (GAM) combined with cokriging of spatial residuals. Specifically, we developed spatial models for nitrogen dioxide (NO(2)) and nitrogen oxides (NO(x)) concentrations in Southern California separately for two seasons (summer and winter) based on over 240 sampling locations. Pollutant concentrations were disaggregated into three components: local means, spatial residuals, and normal random residuals. Local means were modeled by GAM. Spatial residuals were cokriged with global residuals at nearby sampling locations that were spatially auto-correlated. We compared this two-stage approach with four commonly-used spatial models: universal kriging, multiple linear LUR and GAM with and without a spatial smoothing term. Leave-one-out cross validation was conducted for model validation and comparison purposes. The results show that our GAM plus cokriging models predicted summer and winter NO(2) and NO(x) concentration surfaces well, with cross validation R(2) values ranging from 0.88 to 0.92. While local covariates accounted for partial variance of the measured NO(2) and NO(x) concentrations, spatial autocorrelation accounted for about 20% of the variance. Our spatial GAM model improved R(2) considerably compared to the other four approaches. Conclusively, our two-stage model captured summer and winter differences in NO(2) and NO(x) spatial distributions in Southern California well. When sampling location selection cannot be optimized for the intended model and fewer covariates are available as predictors for the model, the two-stage model is more robust compared to multiple linear regression models.

Dataset Information

Spatial Autocorrelation Approaches to Testing Residuals from Least Squares Regression.

Publications

Spatial Autocorrelation Approaches to Testing Residuals from Least Squares Regression.

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