Scale-adaptive estimation of mixed geographically weighted regression models

Abstract

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.