Local least absolute deviation estimation of spatially varying coefficient models: robust geographically weighted regression approaches

Abstract

The geographically weighted regression (GWR) has been widely applied to many practical fields for exploring spatial non-stationarity of a regression relationship. However, this method is inherently not robust to outliers due to the least squares criterion in the process of estimation. Outliers commonly exist in data sets and may lead to a distorted estimate of the underlying regression relationship. Using the least absolute deviation criterion, we propose two robust scenarios of the GWR approaches to handle outliers. One is based on the basic GWR and the other is based on the local linear GWR (LGWR). The proposed methods can automatically reduce the impact of outliers on the estimates of the regression coefficients and can be easily implemented with modern computer software for dealing with the linear programming problems. We then conduct simulations to assess the performance of the proposed methods and the results demonstrate that the methods are quite robust to outliers and can retrieve the underlying coefficient surfaces satisfactorily even though the data are seriously contaminated or contain severe outliers.

Keywords:

• spatially varying coefficient model
• geographically weighted regression
• least absolute deviation
• robust GWR
• outlier

Acknowledgements

This research is supported by the National Natural Science Foundation of China (No. 10971161). Zhang's work is also partially supported by the Scientific Research Programmes of Colleges in Xinjiang (No. XJEDU2008S54). We thank the two anonymous reviewers for their insightful comments on the earlier version of manuscript.