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Open AccessArticle

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

Center for Geospatial Information Science, Department of Geographical Sciences, University of Maryland, College Park, MD 20740, USA
Spatial Analysis Research Center, School of Geographical Sciences an Urban Planning, Arizona State University, Tempe, AZ 85281, USA
Center for Geospatial Sciences, School of Public Policy, University of California, Riverside, CA 92521, USA
School of Geographical Sciences, University of Bristol, Bristol BS8 1SS, UK
Author to whom correspondence should be addressed.
ISPRS Int. J. Geo-Inf. 2019, 8(6), 269;
Received: 16 April 2019 / Revised: 23 May 2019 / Accepted: 5 June 2019 / Published: 8 June 2019
(This article belongs to the Special Issue Free and Open Source Tools for Geospatial Analysis and Mapping)
PDF [6867 KB, uploaded 24 June 2019]


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. View Full-Text
Keywords: multiscale; gwr; spatial statistics; heterogeneity; scale; mgwr multiscale; gwr; spatial statistics; heterogeneity; scale; mgwr

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Oshan, T.M.; Li, Z.; Kang, W.; Wolf, L.J.; Fotheringham, A.S. MGWR: A Python Implementation of Multiscale Geographically Weighted Regression for Investigating Process Spatial Heterogeneity and Scale. ISPRS Int. J. Geo-Inf. 2019, 8, 269.

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