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

Abstract

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.

GIS-based spatial modeling of COVID-19 incidence rate in the continental United States

“…Inspired by Oshan et al (2019), who applied MGWR to study the spatial context of obesogenic process in the state of Arizona, and presuming that a multiscale approach would better explain the spatial variability of COVID-19 rate across the United States, we applied and compared the performance of MGWR to four other global or local models. Our results confirmed and extended the findings of the mentioned study as MGWR achieved the highest goodness-of-fit with the most parsimonious model, among others.…”

“…where ̂ is the vector of parameter estimates ( × 1), is the matrix of the selected explanatory variables ( × ), ( ) is the matrix of spatial weights ( × ), and is the vector of observations of the dependent variable ( × 1) (Fotheringham and Oshan, 2016). ( ) is a diagonal matrix that is constructed from the weights of each observation based on its distance from location and is calibrated based on a locally weighted regression (Brunsdon et al, 1998;Fotheringham and Oshan, 2016 Even though GWR can be a great improvement compared to global regression in the context of spatial processes, it still assumes that the scale of all of the involved relationships are constant over space and thus does not allow for analyzing these relationships at different scales (Fotheringham et al, 2017;Oshan et al, 2019). Whereas, in many cases, including COVID-19 spread, this assumption is not valid because different processes are involved with varying spatial scales.…”

Population exposure across central India to PM2.5 derived using remotely sensed products in a three-stage statistical model

“…A GWR model captures spatial heterogeneity by generating a continuous surface of model parameters at every grid cell instead of universal value for all observations (predictor and response variable). We fitted a daily Gaussian GWR model using adaptive bandwidth selection to minimize the Akaike Information Criterion (AIC c ) value using adaptive bi-square kernel in MGWR python 39 given by Eq. ( 3 ).…”

Local modelling of U.S. mortality rates: A multiscale geographically weighted regression approach

“…In order to explore the possible spatial nonstationarity in the determinants of mortality across the United States, the model was calibrated by MGWR using the MGWR 2.2.1 software developed by Oshan, Li, Kang, Wolf, and Fotheringham (2018). 5 The geographic coordinates for the centroid of each county were used as the spatial units for the data, and an adaptive bisquare kernel function was used to define the weights matrix.…”