Geographically Weighted Quantile Regression

Abstract

Past decades have received an increasing interest in examining spatial heterogeneity or non-stationarity (where the relationships among variables are not stable over space), a “local” spatial association, in the field of geostatistics. An emergent advanced exploratory spatial analytic tool, geographically weighted regression (GWR) has been widely used to implement this task by means of local regression and smoothing techniques. However, the current GWR is only capable of computing the parameter estimates to the mean function of the conditional distribution of the dependent variable. While the quantile regression (QR) has been known as a statistical technique that moves beyond traditional mean modeling, there is lack of spatial analysis technique which not only permits estimating various conditional quantile functions but also allows for exploring spatial non-stationarity. The goal of this study seeks to develop a novel geostatistical approach, geographically weighted quantile regression (GWQR), which integrate the features of QR into the GWR framework. We briefly review GWR and QR, respectively, and then outline their synergy and the new approach GWQR. The proposed method is applied to the U.S. county-level mortality data to demonstrate its usefulness towards exploratory spatial quantile-based analyses.