Exploring heterogeneity and dynamics of meteorological influences on US PM_2.5: A distributed learning approach with spatiotemporal varying coefficient models

Particulate matter (PM) has emerged as a primary air quality concern due to its substantial impact on human health. Many recent research works suggest that PM_2.5 concentrations depend on meteorological conditions. Enhancing current pollution control strategies necessitates a more holistic comprehension of PM_2.5 dynamics and the precise quantification of spatiotemporal heterogeneity in the relationship between meteorological factors and PM_2.5 levels. The spatiotemporal varying coefficient model stands as a prominent spatial regression technique adept at addressing this heterogeneity. Amidst the challenges posed by the substantial scale of modern spatiotemporal datasets, we propose a pioneering distributed estimation method (DEM) founded on multivariate spline smoothing across a domain's triangulation. This DEM algorithm ensures an easily implementable, highly scalable, and communication-efficient strategy, demonstrating almost linear speedup potential. We validate the effectiveness of our proposed DEM through extensive simulation studies, demonstrating that it achieves coefficient estimations akin to those of global estimators derived from complete datasets. Applying the proposed model and method to the US daily PM_2.5 and meteorological data, we investigate the influence of meteorological variables on PM_2.5 concentrations, revealing both spatial and seasonal variations in this relationship.