Non-Iterative Estimation of Multiscale Geographically and Temporally Weighted Regression Model

The Multiscale Geographically and Temporally Weighted Regression model overcomes the limitation of estimating spatiotemporal variation characteristics of regression coefficients for different variables under a single scale, making it a powerful tool for exploring the spatiotemporal scale characteris...

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Main Authors: Ya-Di Dai, Hui-Guo Zhang
Format: Article
Language:English
Published: MDPI AG 2025-04-01
Series:Mathematics
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Online Access:https://www.mdpi.com/2227-7390/13/9/1446
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author Ya-Di Dai
Hui-Guo Zhang
author_facet Ya-Di Dai
Hui-Guo Zhang
author_sort Ya-Di Dai
collection DOAJ
description The Multiscale Geographically and Temporally Weighted Regression model overcomes the limitation of estimating spatiotemporal variation characteristics of regression coefficients for different variables under a single scale, making it a powerful tool for exploring the spatiotemporal scale characteristics of regression relationships. Currently, the most widely used estimation method for multiscale spatiotemporal geographically weighted models is the backfitting-based iterative approach. However, the iterative process of this method leads to a substantial computational burden and the accumulation of errors during iteration. This paper proposes a non-iterative estimation method for the MGTWR model, combining local linear fitting and two-step weighted least squares estimation techniques. Initially, a reduced bandwidth is used to fit a local linear GTWR model to obtain the initial estimates. Then, for each covariate, the optimal bandwidth and regression coefficients are estimated by substituting the initial estimates into a localized least squares problem. Simulation experiments are conducted to evaluate the performance of the proposed non-iterative method compared to traditional methods and the backfitting-based approach in terms of coefficient estimation accuracy and computational efficiency. The results demonstrate that the non-iterative estimation method for MGTWR significantly enhances computational efficiency while effectively capturing the scale effects of spatiotemporal variation in the regression coefficient functions for each predictor.
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spelling doaj-art-f8e04736e8ea4f55a31aaf0f632b4dbb2025-08-20T01:49:11ZengMDPI AGMathematics2227-73902025-04-01139144610.3390/math13091446Non-Iterative Estimation of Multiscale Geographically and Temporally Weighted Regression ModelYa-Di Dai0Hui-Guo Zhang1Department of Statisticss, School of Mathematics and Systems Science, Xinjiang University, Urumqi 830017, ChinaDepartment of Statisticss, School of Mathematics and Systems Science, Xinjiang University, Urumqi 830017, ChinaThe Multiscale Geographically and Temporally Weighted Regression model overcomes the limitation of estimating spatiotemporal variation characteristics of regression coefficients for different variables under a single scale, making it a powerful tool for exploring the spatiotemporal scale characteristics of regression relationships. Currently, the most widely used estimation method for multiscale spatiotemporal geographically weighted models is the backfitting-based iterative approach. However, the iterative process of this method leads to a substantial computational burden and the accumulation of errors during iteration. This paper proposes a non-iterative estimation method for the MGTWR model, combining local linear fitting and two-step weighted least squares estimation techniques. Initially, a reduced bandwidth is used to fit a local linear GTWR model to obtain the initial estimates. Then, for each covariate, the optimal bandwidth and regression coefficients are estimated by substituting the initial estimates into a localized least squares problem. Simulation experiments are conducted to evaluate the performance of the proposed non-iterative method compared to traditional methods and the backfitting-based approach in terms of coefficient estimation accuracy and computational efficiency. The results demonstrate that the non-iterative estimation method for MGTWR significantly enhances computational efficiency while effectively capturing the scale effects of spatiotemporal variation in the regression coefficient functions for each predictor.https://www.mdpi.com/2227-7390/13/9/1446multiscale GTWRlocal linear estimatorspatiotemporal non-stationarityspatiotemporal regressionnonparametric estimation
spellingShingle Ya-Di Dai
Hui-Guo Zhang
Non-Iterative Estimation of Multiscale Geographically and Temporally Weighted Regression Model
Mathematics
multiscale GTWR
local linear estimator
spatiotemporal non-stationarity
spatiotemporal regression
nonparametric estimation
title Non-Iterative Estimation of Multiscale Geographically and Temporally Weighted Regression Model
title_full Non-Iterative Estimation of Multiscale Geographically and Temporally Weighted Regression Model
title_fullStr Non-Iterative Estimation of Multiscale Geographically and Temporally Weighted Regression Model
title_full_unstemmed Non-Iterative Estimation of Multiscale Geographically and Temporally Weighted Regression Model
title_short Non-Iterative Estimation of Multiscale Geographically and Temporally Weighted Regression Model
title_sort non iterative estimation of multiscale geographically and temporally weighted regression model
topic multiscale GTWR
local linear estimator
spatiotemporal non-stationarity
spatiotemporal regression
nonparametric estimation
url https://www.mdpi.com/2227-7390/13/9/1446
work_keys_str_mv AT yadidai noniterativeestimationofmultiscalegeographicallyandtemporallyweightedregressionmodel
AT huiguozhang noniterativeestimationofmultiscalegeographicallyandtemporallyweightedregressionmodel