mgwr: A Python Implementation of Multiscale Geographically Weighted Regression for Investigating Process Spatial Heterogeneity and Scale

TLDR

Geographically weighted regression (GWR) is a spatial statistical technique that addresses the limitations of global models by allowing effects to vary over space, capturing spatial heterogeneity, and its recent multiscale extension permits each relationship to vary at distinct spatial scales. This paper introduces mgwr, a Python implementation of multiscale GWR that focuses on multiscale analysis of spatial heterogeneity. mgwr calibrates local linear models across locations using nearby data, producing spatially varying parameter surfaces and a bandwidth parameter that indicates process scale, and includes case studies, core concept reviews, and a literate programming style overview of functionality and usage. The package provides novel inference and exploratory analysis tools, unique diagnostics for multi‑scale local models, and dramatic improvements in estimation efficiency.

Abstract

Geographically weighted regression (GWR) is a spatial statistical technique that recognizes that traditional ‘global’ regression models may be limited when spatial processes vary with spatial context. GWR captures process spatial heterogeneity by allowing effects to vary over space. To do this, GWR calibrates an ensemble of local linear models at any number of locations using ‘borrowed’ nearby data. This provides a surface of location-specific parameter estimates for each relationship in the model that is allowed to vary spatially, as well as a single bandwidth parameter that provides intuition about the geographic scale of the processes. A recent extension to this framework allows each relationship to vary according to a distinct spatial scale parameter, and is therefore known as multiscale (M)GWR. This paper introduces mgwr, a Python-based implementation of MGWR that explicitly focuses on the multiscale analysis of spatial heterogeneity. It provides novel functionality for inference and exploratory analysis of local spatial processes, new diagnostics unique to multi-scale local models, and drastic improvements to efficiency in estimation routines. We provide two case studies using mgwr, in addition to reviewing core concepts of local models. We present this in a literate programming style, providing an overview of the primary software functionality and demonstrations of suggested usage alongside the discussion of primary concepts and demonstration of the improvements made in mgwr.