Bayesian modelling of longitudinal data with space-time interaction and bootstrap analysis
DOI:
https://doi.org/10.64497/jssci.174Keywords:
Bayesian spatio-temporal model, Spatial effect, Temporal effect, Interaction effect, Hierarchical Bayesian modeling, Bootstrap analysisAbstract
This paper presents a Bayesian spatio-temporal model with space-time interaction effects for longitudinal data. The main objective is to evaluate how spatial and temporal dependencies, together with their interactions, influence parameter estimation and interpretation. The model incorporates spatial random effects to capture unobserved heterogeneity between neighboring regions, temporal random effects to reflect trends over time, and interaction terms to account for localized space-time variations. A conditional autoregressive (CAR) prior is applied to address spatial dependence, while Markov chain Monte Carlo (MCMC) sampling is used for posterior estimation, supported by convergence diagnostics such as trace plots and the Geweke test. Bootstrap analysis is also applied to assess the stability of estimates and provide complementary validation. Results based on simulated datasets across multiple areal unit sizes show that the intercept and covariate effects are sensitive to spatial resolution, whereas spatial and temporal correlations remain relatively stable across scales. The variance components, particularly the interaction term, capture localized heterogeneity more effectively at smaller spatial units. The findings demonstrate that combining Bayesian estimation with bootstrap analysis provides a reliable framework for understanding spatial and temporal disease dynamics, with practical implications for public health planning and intervention strategies.
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Copyright (c) 2026 Aliyu Abba Mustapha, Hani Syahida Zulkafli, Jayanthi Arasan, Mohammed Abba Mustapha
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