Statistics and Computational Methods Seminar Series - 2024/25

Speaker: Amira Elayouty (Cairo University, Egypt)

Title: Multi-scale Geographically Weighted Quantile Regression

Abstract

Spatial non-stationarity and spatial autocorrelation are two typical properties of spatial data. Geographically Weighted Regression (GWR) is one class of models which explores and accounts for the potential non-stationarity of relationships between a response and some explanatory variables across space. In some situations, heterogeneity does not only arise from the non-stationarity of data relationships over space but also from the response heterogeneity across different locations of the outcome distribution. This leads to the rise of Geographically Weighted Quantile Regression (GWQR) which accounts for both sources of heterogeneity and provides an entire description of the response distribution across space. However, GWQR assumes that modelled processes operate at the same spatial scale. This is an unrealistic assumption for spatially varying relationships that may operate at different spatial scales. Therefore, we introduce a Multi-scale Geographically Weighted Quantile Regression (MGWQR) that relaxes the assumption that all relationships operate at the same scale. This proposed methodology relies on estimating a vector of optimal bandwidths measuring the spatial scales at which the different processes (relationships) operate at each quantile. The estimation of the model and the selection of the vector of bandwidths in MGWQR are implemented using a back-fitting algorithm. The performance of the proposed model is evaluated against the existing GWQR with means of a simulation study and an empirical illustration. The application considers the impacts of a set of climate variables on children’s health and growth data in Uganda.