A bootstrap test for constant coefficients in geographically weighted regression models

ABSTRACT

Statistical tests for whether some coefficients really vary over space play an important role in using the geographically weighted regression (GWR) to explore spatial non-stationarity of the regression relationship. In view of some shortcomings of the existing inferential methods, we propose a residual-based bootstrap test to detect the constant coefficients in a GWR model. The proposed test is free of the assumption that the model error term is normally distributed and admits some useful extensions for identifying more complicated spatial patterns of the coefficients. Some simulation with comparison to the existing test methods is conducted to assess the test performance, including the accuracy of the bootstrap approximation to the null distribution of the test statistic, the power in identifying spatially varying coefficients and the robustness to collinearity among the explanatory variables. The simulation results demonstrate that the bootstrap test works quite well. Furthermore, a real-world data set is analyzed to illustrate the application of the proposed test.

KEYWORDS:

• Geographically weighted regression
• spatial non-stationarity
• generalized likelihood ratio statistic
• bootstrap

Acknowledgements

The authors thank the reviewers for their helpful comments and suggestions, which lead to a great deal of improvement on the manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

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Funding

This work was supported by the National Natural Science Foundation of China [No. 11271296].