Structure identification and variable selection in geographically weighted regression models

ABSTRACT

Geographically weighted regression (GWR) is an important tool for exploring spatial non-stationarity of a regression relationship, in which whether a regression coefficient really varies over space is especially important in drawing valid conclusions on the spatial variation characteristics of the regression relationship. This paper proposes a so-called GWGlasso method for structure identification and variable selection in GWR models. This method penalizes the loss function of the local-linear estimation of the GWR model by the coefficients and their partial derivatives in the way of the adaptive group lasso and can simultaneously identify spatially varying coefficients, nonzero constant coefficients and zero coefficients. Simulation experiments are further conducted to assess the performance of the proposed method and the Dublin voter turnout data set is analysed to demonstrate its application.

KEYWORDS:

• Geographically weighted regression
• spatial non-stationarity
• adaptive group lasso
• structure identification
• variable selection

Acknowledgments

The authors thank the Associate Editor and the referee for their many insightful and inspiring comments and suggestions which greatly improved the paper, and also thank Professor Jingxiao Zhang for beneficial discussions.

Disclosure statement

No potential conflict of interest was reported by the authors.