Multiscale geographically weighted quantile regression

Abstract

Spatial heterogeneity across multiple scales is a common issue in various disciplines including economics and public health. Geographically weighted quantile regression (GWQR) addresses this by assuming the same spatial scale for all modelled processes at each quantile. This paper introduces a multiscale geographically weighted quantile regression (MGWQR) that allows different processes to operate at different spatial scales at each quantile across the entire response distribution. The methodology estimates optimal bandwidths at each quantile of the response distribution using a back-fitting algorithm, with the selection of bandwidths done within the algorithm using the golden search optimisation method. Simulation study and a real-world example, that considers analysing the impacts of a set of socioeconomic and climate variables on children’s stunting, show that MGWQR outperforms GWQR and QR models.