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...
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MDPI AG
2023-02-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/25/2/320 |
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| author | Shi-Jie Gao Chang-Lin Mei Qiu-Xia Xu Zhi Zhang |
| author_facet | Shi-Jie Gao Chang-Lin Mei Qiu-Xia Xu Zhi Zhang |
| author_sort | Shi-Jie Gao |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-03-11T08:51:40Z |
| format | Article |
| id | doaj.art-429f7e2478104fd28a933e0f153c90fb |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-11T08:51:40Z |
| publishDate | 2023-02-01 |
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| spelling | doaj.art-429f7e2478104fd28a933e0f153c90fb2023-11-16T20:23:52ZengMDPI AGEntropy1099-43002023-02-0125232010.3390/e25020320Non-Iterative Multiscale Estimation for Spatial Autoregressive Geographically Weighted Regression ModelsShi-Jie Gao0Chang-Lin Mei1Qiu-Xia Xu2Zhi Zhang3Department of Finance and Statistics, School of Science, Xi’an Polytechnic University, Xi’an 710048, ChinaDepartment of Finance and Statistics, School of Science, Xi’an Polytechnic University, Xi’an 710048, ChinaDepartment of Finance and Statistics, School of Science, Xi’an Polytechnic University, Xi’an 710048, ChinaDepartment of Statistics, School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, ChinaMultiscale 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.https://www.mdpi.com/1099-4300/25/2/320geographically weighted regressionspatial autoregressive geographically weighted regression modelmultiscale estimationspatial scale |
| spellingShingle | Shi-Jie Gao Chang-Lin Mei Qiu-Xia Xu Zhi Zhang Non-Iterative Multiscale Estimation for Spatial Autoregressive Geographically Weighted Regression Models Entropy geographically weighted regression spatial autoregressive geographically weighted regression model multiscale estimation spatial scale |
| 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 | geographically weighted regression spatial autoregressive geographically weighted regression model multiscale estimation spatial scale |
| url | https://www.mdpi.com/1099-4300/25/2/320 |
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