A Bayesian State-Space Approach to Dynamic Hierarchical Logistic Regression for Evolving Student Risk in Educational Analytics

Early detection of academically at-risk students is crucial for designing timely interventions that improve educational outcomes. However, many existing approaches either ignore the temporal evolution of student performance or rely on “black box” models that sacrifice interpretability. In this study, we develop a dynamic hierarchical logistic regression model in a fully Bayesian framework to address these shortcomings. Our method leverages partial pooling across students and employs a state-space formulation, allowing each student’s log-odds of failure to evolve over multiple assessments. By using Markov chain Monte Carlo for inference, we obtain robust posterior estimates and credible intervals for both population-level and individual-specific effects, while posterior predictive checks ensure model adequacy and calibration. Results from simulated and real-world datasets indicate that the proposed approach more accurately tracks fluctuations in student risk compared to static logistic regression, and it yields interpretable insights into how engagement patterns and demographic factors influence failure probability. We conclude that a Bayesian dynamic hierarchical model not only enhances prediction of at-risk students but also provides actionable feedback for instructors and administrators seeking evidence-based interventions.