mgwr: A Python implementation of multiscale geographically weighted regression for investigating process spatial heterogeneity and scale

Geographically weighted regression (GWR) is a spatial statistical technique that recognizes traditional 'global' regression models may be limited when spatial processes vary with spatial context. GWR captures process spatial heterogeneity via an operationalization of Tobler's first law of geography: "everything is related to everything else, but near things are more related than distant things" (1970). An ensemble of local linear models are calibrated at any number of locations by 'borrowing' nearby data. The result is a surface of location-specific parameter estimates for each relationship in the model that may 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 for efficiently calibrating a variety of (M)GWR models and a selection of associated diagnostics. It reviews some core concepts, introduces the primary software functionality, and demonstrates suggested usage on several example datasets.