Non-Iterative Estimation of Multiscale Geographically and Temporally Weighted Regression Model - Ya-Di Dai; Hui-Guo Zhang (Mathematics)
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.