Multiscale Geographically Weighted Regression (MGWR)

Fotheringham, A. Stewart; Yang, Wenbai; Kang, Wei

doi:10.1080/24694452.2017.1352480

Cited by 619 publications

(725 citation statements)

References 25 publications

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“…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.…”

Section: Spatial Error Model (Sem)mentioning

confidence: 99%

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

Mollalo

Vahedi

Rivera

2020

Science of The Total Environment

591

584

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Journal Pre-proof J o u r n a l P r e -p r o o f 2 GIS-based Spatial Modeling of COVID-19 Incidence Rate in the Continental United States AbstractDuring the first 90 days of the COVID-19 outbreak in the United States, over 675,000 confirmed cases of the disease have been announced, posing unprecedented socioeconomic burden to the country. Due to inadequate research on geographic modeling of COVID-19, we investigated county-level variations of disease incidence across the continental United States. We compiled a geodatabase of 35 environmental, socioeconomic, topographic, and demographic variables that could explain the spatial variability of disease incidence. Further, we employed spatial lag and spatial error models to investigate spatial dependence and geographically weighted regression (GWR) and multiscale GWR (MGWR) models to locally examine spatial non-stationarity. The results suggested that even though incorporating spatial autocorrelation could significantly improve the performance of the global ordinary least square model; these models still represent a significantly poor performance compared to the local models. Moreover, MGWR could explain the highest variations (adj. R 2 : 68.1%) with the lowest AICc compared to the others. Mapping the effects of significant explanatory variables (i.e., income inequality, median household income, the proportion of black females, and the proportion of nurse practitioners) on spatial variability of COVID-19 incidence rates using MGWR could provide useful insights to policymakers for targeted interventions.

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Section: Spatial Error Model (Sem)mentioning

confidence: 99%

“…MGWR is an extension of GWR that allows studying the relationships at varying spatial scales and achieves that by using varying bandwidth as opposed to a single, constant bandwidth for the entire study area (Fotheringham et al, 2017;Yu et al, 2019). MGWR can be formulated as (Fotheringham et al, 2017)…”

Section: Spatial Error Model (Sem)mentioning

confidence: 99%

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

Mollalo

Vahedi

Rivera

2020

Science of The Total Environment

591

584

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“…The selected set of variables was then used to explain the spatial pattern of residuals from the pooled niche model using MGWR (https://sgsup.asu.edu/sparc/multiscale-gwr), implemented in Python 2.7.10 (Python Software Foundation; http://www.python.org) with the “mgwr” package (Oshan, Li, Kang, Wolf, & Fotheringham, ) with adaptive bandwidths. MGWR uses an iterative back‐fitting algorithm that is computationally intensive (Fotheringham et al, ). We therefore thinned the calibration data to 3 per 10 km 2 to reduce computation time, resulting in a dataset with 2,156 records.…”

Section: Methodsmentioning

confidence: 99%

“…However, previous implementations of GWR have required a single bandwidth for all explanatory variables (Fotheringham et al, ), thus precluding a multi‐scale approach. A recent development has enabled estimation of separate spatial scales for each explanatory variable by optimizing multiple bandwidth parameters—multiscale geographically weighted regression (MGWR; Fotheringham, Yang, & Kang, ), which allows a multi‐scale approach to exploring species–environment relationships.…”

Section: Introductionmentioning

confidence: 99%

Local niche differences predict genotype associations in sister taxa of desert tortoise

Inman

Fotheringham

Franklin

et al. 2019

Diversity and Distributions

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Aims To investigate spatial congruence between ecological niches and genotype in two allopatric species of desert tortoise that are species of conservation concern. Location Mojave and Sonoran Desert ecoregions; California, Nevada, Arizona, Utah, USA. Methods We compare ecological niches of Gopherus agassizii and Gopherus morafkai using species distribution modelling (SDM) and then calibrate a pooled‐taxa distribution model to explore local differences in species–environment relationships based on the spatial residuals of the pooled‐taxa model. We use multiscale geographically weighted regression (MGWR) applied to those residuals to estimate local species–environment relationships that can vary across the landscape. We identify multivariate clusters in these local species–environment relationships and compare them against models of (a) a geographically based taxonomic designation for two sister species and (b) an environmental ecoregion designation, with respect to their ability to predict a genotype association index for these two species. Results We find non‐identical niches for these species, with differences that span physiographic and vegetation niche dimensions. We find evidence for two distinct clusters of local species–environment relationships that when mapped, predict an index of genotype association for the two sister taxa better than did either the geographically based taxonomic designation or an environmental ecoregion designation. Main conclusions Exploring local species–environment relationships by coupling SDM and MGWR can benefit studies of biogeography and conservation. We find that niche separation in habitat selection conforms to genotypic differences between sister taxa of tortoise in a recent secondary contact zone. This result may inform decision making by agencies with regulatory or land management authority for the two sister taxa addressed here.

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“…For example, Gelman (2007) finds that the estimated effect of income on vote choice changes depending on the state in a multilevel model. For geographers, this change in model parameters over a geography is usually called nonstationarity (Fotheringham, 1997), and has been studied extensively in a large variety of local model specifications (Casetti, 1972;Paez et al, 2002;Gelfand et al, 2003;Fotheringham et al, 2004;Rue and Held, 2005;Griffith, 2008;Finley, 2011;Fotheringham et al, 2017;Wolf et al, 2018b). These local models provide distinct parameter estimates at every observation.…”

Section: Introductionmentioning

confidence: 99%

On Spatial and Platial Dependence: Examining Shrinkage in Spatially-Dependent Multilevel Models

Wolf¹,

Anselin²,

Arribas‐Bel³

et al. 2018

Preprint

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This paper examines spatially-correlated multilevel models from formal/mathematical and empirical perspectives. Multilevel (or variance components) models have been applied in many areas of regional science, school effect estimation, epidemiology, and polimetrics. They are most often used to model treatment nonstationarity in policy regimes, a form of spatial process heterogeneity. Multilevel models with spatially-correlated components are increasingly used to model the joint presence of spatial heterogeneity and spatial dependence. Previous treatments typically focus on stating a single spatial multilevel specification, deriving its estimators, and demonstrating its properties in a case study. Instead, a more general approach is possible. To do this, we derive the "shrinkage matrix," which directly expresses the relationship between single-level model estimates and their multilevel analogues. We show that this shrinkage matrix results in regional spatial spillovers, a substantial novel behavior. We provide an empirical example that demonstrates this behavior: identifying state-specific factors influencing endoscopy use among Medicare participants. Due to the complexity of tradeoffs between dependence and heterogeneity in even simple spatial multilevel models, we suggest more formal attention is needed to build transferable insight in this area. *

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Multiscale Geographically Weighted Regression (MGWR)

Cited by 619 publications

References 25 publications

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

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

Local niche differences predict genotype associations in sister taxa of desert tortoise

On Spatial and Platial Dependence: Examining Shrinkage in Spatially-Dependent Multilevel Models

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