Scale-adaptive estimation of mixed geographically weighted regression models

Mixed geographically weighted regression (GWR) models, a combination of linear and spatially varying coefficient models, have found their applications in a variety of disciplines including economic modelling for geo-referenced data analysis. Generally, different explanatory variables may operate at different spatial scales, leading to different levels of spatial heterogeneity of the varying coefficients. To deal with such a multiscale problem, we propose a scale-adaptive method to calibrate mixed GWR models, in which a different bandwidth is separately assumed for each spatially varying coefficient and is selected based on the backfitting procedure. Extensive simulations with different spatial layouts and a real-world example based on the Dublin voter turnout data demonstrate that the scale-adaptive method can not only significantly improve the estimation accuracy of the spatially varying coefficients, but also provide valuable information on the scale at which each explanatory variable operates.

Automated summary

An adaptive scale method is proposed to improve the estimation accuracy of mixed GWR models and provide valuable information on the operating scale of explanatory variables.