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

Ya-Di Dai and Hui-Guo Zhang ()
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Ya-Di Dai: Department of Statisticss, School of Mathematics and Systems Science, Xinjiang University, Urumqi 830017, China
Hui-Guo Zhang: Department of Statisticss, School of Mathematics and Systems Science, Xinjiang University, Urumqi 830017, China

Mathematics, 2025, vol. 13, issue 9, 1-16

Abstract: 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.

Keywords: multiscale GTWR; local linear estimator; spatiotemporal non-stationarity; spatiotemporal regression; nonparametric estimation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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