Inference issue in multiscale geographically and temporally weighted regression

文献类型： 外文期刊

第一作者： Hong, Zhimin

作者： Hong, Zhimin;Wang, Ruoxuan;Wang, Zhiwen;Hong, Zhimin;Du, Wala;Du, Wala

作者机构：

关键词： Geographically and temporally weighted regression; Spatiotemporal heterogeneity; Standard deviation; Hat matrix; Scale effect

期刊名称：STATISTICS AND COMPUTING （ 影响因子：1.6； 五年影响因子：2.2 ）

ISSN： 0960-3174

年卷期： 2025 年 35 卷 2 期

页码：

收录情况： SCI

摘要： Geographically and temporally weighted regression (GTWR) models assume that all of the varying coefficients operate at a same spatiotemporal scale, which reduces the flexibility of local regression models. Multiscale geographically and temporally weighted regression (MGTWR) models increase flexibility, enhance interpretability, and provide more comprehensive information by allowing regression coefficients to vary across different spatiotemporal scales. However, a limitation of the MGTWR models is that, to date, statistical inference regarding the local coefficient estimates has not been feasible. Formally, "hat matrix", which projects the observed response variable vector onto the fitting response variable, was not available in the MGTWR model. This paper settles this limitation by reformulating the GTWR model into a Generalized Additive Model, extending this framework to the MGTWR model and then deriving standard deviations for the local coefficient estimates in the MGTWR model. In addition, we also obtain the number of effective parameters for the overall fit of the MGTWR model and for each covariate within the model. This statistic is crucial for comparing the goodness of fit between MGTWR, GTWR and classical global regression models, as well as for adjusting multiple tests. Simulation studies and a real-world example demonstrate these advances to the MGTWR framework.

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