Spatiotemporally Varying Coefficients (STVC) model: a Bayesian local regression to detect spatial and temporal nonstationarity in variables relationships

Abstract

Local regression has an advantage over global regression by allowing coefficients that qualify variables relationships being heterogeneous, where such varying regression relationships are nonstationarity. Spatiotemporally Varying Coefficients (STVC) model is the first Bayesianbased local spatiotemporal regression approach, intending to simultaneously detect spatial and temporal nonstationarity for heterogeneous response-covariate variables relationships, through separately estimating posterior local-scale coefficients over different space areas and time frames. In this paper, we first presented a general Bayesian STVC modelling paradigm as a specification guide to show its commonality in broader geospatial research. Then, we employed it to solve a real-world issue concerning spatiotemporal healthcare-socioeconomic relations, for which we derived data of county-level hospital beds number per capita, as well as data of related socioeconomic factors in northeast China during 2002-2011. Results showed that the STVC model surpassed all the other comparative regressions, in terms of both Bayesian model fitness and predictive ability. Globally, resident savings, financial institutions loans, GDP, and primary industry were identified as key socioeconomic conditions affecting healthcare resources in Northeast China. Temporally, with Time-Coefficients (TC) plots, we found that after 2011, GDP and primary industry would further help improve the overall healthcare level of northeast China. Spatially, with Space-Coefficients (SC) maps, we could directly identify the relative contribution of four socioeconomic covariates' impacts on healthcare within each administrative county. Bayesian STVC model is an essential development and extension of the local regression family for exploring the spatiotemporal heterogeneous variables relationships, especially under Bayesian statistics, as well as GIScience and spatial statistics.

Spatial and Temporal Impacts of Socioeconomic and Environmental Factors on Healthcare Resources: A County-Level Bayesian Local Spatiotemporal Regression Modeling Study of Hospital Beds in Southwest China

“…Spatiotemporally varying coefficients (STVC) model, a Bayesian-based local spatiotemporal regression approach, has been proposed for space-time big data with the core mission of detecting both the spatial and temporal heterogeneous relationships between the response and different covariates variables, via estimating posterior local-scale regression coefficients across space and over time [28,29]. Compared with the global-scale spatiotemporal regression models, the fundamental advantage of the local-scale Bayesian STVC model is further incorporating the spatial-temporal autocorrelated nonstationarity for the observable underlying covariates within the Bayesian hierarchical modeling (BHM) framework, such as the socioeconomic and environmental factors concerned in this case.…”

“…Herein, model 5 is a simplified version of a general STVC model by removing the global-scale stationary fixed effect of auxiliary covariates (same as in model 1), as well as the spatiotemporal random effects of intercepts (same as in model 2). These interpretation-driven STVC settings make sense particularly for exploring the response-covariate relations along with explicit spatial patterns and temporal trends, aiming at explaining the mechanism behind the research object, as it removes the potential interactive influences of local intercepts [29].…”

“…Striving to verify these two hypothetical theories, in this study, we employed a state-of-the-art local spatiotemporal regression approach, namely, a Bayesian spatiotemporally varying coefficients (STVC) model, to innovatively quantify and characterize the spatial and temporal heterogeneous associations of county-level hospital beds with multiple socioeconomic and environmental covariates across southwest China from 2002 to 2011. The STVC model is a Bayesian-based local spatiotemporal regression proposed for space-time big data, which was aimed at simultaneous detection of spatial and temporal autocorrelated nonstationarity in heterogeneous response-covariate variables relationships [28,29]. Both Bayesian statistics theories and hierarchical modeling frameworks are adopted in this real "full map" modeling approach, along with a space-time independent nonstationary assumption that is achieved by separately estimating posterior local-scale coefficients over different space areas and time points [29].…”

“…The STVC model is a Bayesian-based local spatiotemporal regression proposed for space-time big data, which was aimed at simultaneous detection of spatial and temporal autocorrelated nonstationarity in heterogeneous response-covariate variables relationships [28,29]. Both Bayesian statistics theories and hierarchical modeling frameworks are adopted in this real "full map" modeling approach, along with a space-time independent nonstationary assumption that is achieved by separately estimating posterior local-scale coefficients over different space areas and time points [29].…”

Spatiotemporal Distribution Characteristics and Driving Forces of PM2.5 in Three Urban Agglomerations of the Yangtze River Economic Belt

“…Recent advancements in spatial robustness research have led to rapid developments in geostatistical models, such as the GWR [ 29 , 30 ] and LUR [ 31 ] models based on improved strategies. Further, models such as PCA-GWR, Multiscale Geographically Weighted Regression (MGWR), Geographically and Temporally Weighted (GTWR), and the geostatistical model combined with machine learning have produced more reliable regression results at spatiotemporal scales [ 32 , 33 , 34 , 35 ]. Due to the differences in their data sources, study areas, and influencing factor selection, however, such models can result in inconsistent conclusions.…”