Spatiotemporal Heterogeneity Learning: Generalized SpatioTemporal Semi-Varying Coefficient Models With Structure Identification.

This paper proposes a class of Generalized SpatioTemporal Semi-Varying Coefficient Models (GST-SVCMs) with structure identification to enhance the detection and interpretation of spatiotemporal heterogeneity in factors influencing response variables. The proposed framework effectively distinguishes between spatiotemporally varying and constant effects, addressing a key limitation of current modeling approaches. By identifying and separating these components, the GST-SVCM structure identification method improves both computational efficiency and the statistical power of downstream analyses. The estimators of constant coefficients and varying coefficient functions are consistent, and the estimators of the constant coefficients are asymptotically normal, facilitating reliable statistical inference. Extensive Monte Carlo simulations demonstrate that the proposed method accurately identifies the true model structure and significantly improves prediction accuracy compared to purely varying coefficient models that do not incorporate structure identification. To further refine model granularity, we extend GST-SVCMs by introducing the Hierarchical Spatiotemporal Varying Coefficient Model (HSTVCM) with automatic structure identification, which decomposes effects into spatial, temporal, and spatiotemporal components for more precise structure identification. The practical utility of the proposed methodologies is validated through an application to particulate matter (PM) data, providing insights into the influence of meteorological factors on PM levels and determining whether these effects exhibit true spatiotemporal variation.