A two-stage unified Bayesian framework for adolescent physical fitness surveillance in Sichuan, China: Latent factor measurement followed by spatiotemporal modeling.

Large-scale adolescent fitness testing produces heterogeneous multi-item measurements. Translating these measurements into interpretable and comparable evidence for provincial surveillance remains challenging. We propose a two-stage Bayesian framework for adolescent physical fitness surveillance in Sichuan, China. In Stage 1, Bayesian confirmatory factor analysis maps cross-grade test items onto four latent fitness factors: strength, speed, endurance, and flexibility. This stage explicitly models item-level measurement error and item heterogeneity. In Stage 2, factor-level outcomes are modeled using Bayesian spatiotemporal hierarchical regression. This stage estimates covariate associations, temporal trends, and residual spatial heterogeneity. In the Sichuan application, the four latent factors showed clear and interpretable spatial structure. Residual spatial clustering persisted after adjustment for covariates, educational-stage effects, and shared temporal trends. Urbanization rate showed positive conditional associations with all four factors. Selected socioeconomic, geographic, and environmental covariates showed domain-specific associations, such as negative associations of GDP per capita and population density mainly with strength and speed. Model comparison using PSIS-LOO indicated that models with spatial random effects provided better conditional pointwise predictive fit than corresponding no-spatial models for all four factors, with satisfactory Pareto-k diagnostics. By separating latent measurement from regional spatiotemporal modeling, the proposed framework supports more interpretable regional comparisons. It also helps identify regions with persistent residual advantages or disadvantages, providing quantitative evidence for targeted monitoring and policy discussion.