An efficient calibration algorithm for multiscale geographically and temporally weighted regression

Multiscale geographically and temporally weighted regression (MGTWR) is widely applied to address spatiotemporal heterogeneity and relationships at different scales in domains such as land use, urban vitality, and transportation. However, conventional MGTWR calibration, relying on locally weighted least squares and the back-fitting algorithm, faces two key limitations: boundary effects (i. e. edge bias) and high computational cost. To address these issues, this study proposes an efficient calibration algorithm for MGTWR, termed the Two-Step Calibration Algorithm based on local linear fitting (MGTWR₂SCALL). By exploiting the local linear structure via Taylor series expansion, MGTWR₂SCALL performs model calibration through a two-stage local smoothing procedure, eliminating the need for the iterative back-fitting process. The algorithm’s performance is rigorously evaluated through simulation experiments and a real-world case study analyzing carbon emissions in China during 2014–2021. The results demonstrate that MGTWR₂SCALL effectively mitigates boundary effects and enhances computational efficiency. Thus, MGTWR₂SCALL offers substantial theoretical and practical significance for advancing spatiotemporal statistical modeling.