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Non-Iterative Multiscale Estimation for Spatial Autoregressive Geographically Weighted Regression Models
Multiscale estimation for geographically weighted regression (GWR) and the related models has attracted much attention due to their superiority. This kind of estimation method will not only improve the accuracy of the coefficient estimators but also reveal the underlying spatial scale of each explan...
Autores principales: | , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2023
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9954997/ https://www.ncbi.nlm.nih.gov/pubmed/36832686 http://dx.doi.org/10.3390/e25020320 |
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author | Gao, Shi-Jie Mei, Chang-Lin Xu, Qiu-Xia Zhang, Zhi |
author_facet | Gao, Shi-Jie Mei, Chang-Lin Xu, Qiu-Xia Zhang, Zhi |
author_sort | Gao, Shi-Jie |
collection | PubMed |
description | Multiscale estimation for geographically weighted regression (GWR) and the related models has attracted much attention due to their superiority. This kind of estimation method will not only improve the accuracy of the coefficient estimators but also reveal the underlying spatial scale of each explanatory variable. However, most of the existing multiscale estimation approaches are backfitting-based iterative procedures that are very time-consuming. To alleviate the computation complexity, we propose in this paper a non-iterative multiscale estimation method and its simplified scenario for spatial autoregressive geographically weighted regression (SARGWR) models, a kind of important GWR-related model that simultaneously takes into account spatial autocorrelation in the response variable and spatial heterogeneity in the regression relationship. In the proposed multiscale estimation methods, the two-stage least-squares (2SLS) based GWR and the local-linear GWR estimators of the regression coefficients with a shrunk bandwidth size are respectively taken to be the initial estimators to obtain the final multiscale estimators of the coefficients without iteration. A simulation study is conducted to assess the performance of the proposed multiscale estimation methods, and the results show that the proposed methods are much more efficient than the backfitting-based estimation procedure. In addition, the proposed methods can also yield accurate coefficient estimators and such variable-specific optimal bandwidth sizes that correctly reflect the underlying spatial scales of the explanatory variables. A real-life example is further provided to demonstrate the applicability of the proposed multiscale estimation methods. |
format | Online Article Text |
id | pubmed-9954997 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2023 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-99549972023-02-25 Non-Iterative Multiscale Estimation for Spatial Autoregressive Geographically Weighted Regression Models Gao, Shi-Jie Mei, Chang-Lin Xu, Qiu-Xia Zhang, Zhi Entropy (Basel) Article Multiscale estimation for geographically weighted regression (GWR) and the related models has attracted much attention due to their superiority. This kind of estimation method will not only improve the accuracy of the coefficient estimators but also reveal the underlying spatial scale of each explanatory variable. However, most of the existing multiscale estimation approaches are backfitting-based iterative procedures that are very time-consuming. To alleviate the computation complexity, we propose in this paper a non-iterative multiscale estimation method and its simplified scenario for spatial autoregressive geographically weighted regression (SARGWR) models, a kind of important GWR-related model that simultaneously takes into account spatial autocorrelation in the response variable and spatial heterogeneity in the regression relationship. In the proposed multiscale estimation methods, the two-stage least-squares (2SLS) based GWR and the local-linear GWR estimators of the regression coefficients with a shrunk bandwidth size are respectively taken to be the initial estimators to obtain the final multiscale estimators of the coefficients without iteration. A simulation study is conducted to assess the performance of the proposed multiscale estimation methods, and the results show that the proposed methods are much more efficient than the backfitting-based estimation procedure. In addition, the proposed methods can also yield accurate coefficient estimators and such variable-specific optimal bandwidth sizes that correctly reflect the underlying spatial scales of the explanatory variables. A real-life example is further provided to demonstrate the applicability of the proposed multiscale estimation methods. MDPI 2023-02-09 /pmc/articles/PMC9954997/ /pubmed/36832686 http://dx.doi.org/10.3390/e25020320 Text en © 2023 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article Gao, Shi-Jie Mei, Chang-Lin Xu, Qiu-Xia Zhang, Zhi Non-Iterative Multiscale Estimation for Spatial Autoregressive Geographically Weighted Regression Models |
title | Non-Iterative Multiscale Estimation for Spatial Autoregressive Geographically Weighted Regression Models |
title_full | Non-Iterative Multiscale Estimation for Spatial Autoregressive Geographically Weighted Regression Models |
title_fullStr | Non-Iterative Multiscale Estimation for Spatial Autoregressive Geographically Weighted Regression Models |
title_full_unstemmed | Non-Iterative Multiscale Estimation for Spatial Autoregressive Geographically Weighted Regression Models |
title_short | Non-Iterative Multiscale Estimation for Spatial Autoregressive Geographically Weighted Regression Models |
title_sort | non-iterative multiscale estimation for spatial autoregressive geographically weighted regression models |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9954997/ https://www.ncbi.nlm.nih.gov/pubmed/36832686 http://dx.doi.org/10.3390/e25020320 |
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