Early Prediction of Student Performance Using Bayesian Updating with Informative Priors Across Cohorts

Abstract

Early identification of at risk students in higher education depends on predictive models that maintain accuracy across successive cohorts -- a requirement that single-cohort modeling approaches fail to meet. This study evaluates Bayesian updating with informative priors from a previous cohort to improve cross-cohort prediction robustness using digital trace data. We fit weekly Bayesian linear, logistic, and ordinal regression models with either uninformative default priors or informative priors derived from posterior distributions of a preceding cohort. Models were applied to six weekly self-regulated learning (SRL)-aligned engagement indicators from two consecutive cohorts of students in a blended first-year mathematics course (N1 = 307; N2 = 323). Outcomes were exam points, final grades, and a binary at risk indicator. The models were evaluated weekly based on accuracy, sensitivity, and RMSE. In the source cohort, performance was already substantial by week 6. In the target cohort, informative priors improved early classification: Logistic models with priors reduced misclassification by 22% and false negatives by 38% in week 3 relative to the uninformative default. Ordinal models with priors similarly showed the strongest improvements in early weeks, reducing misclassification by 42% in week 2 and reaching an accuracy of .77 by week 4. Linear models showed little benefit from prior information. These findings demonstrate that Bayesian updating is a viable method for improving early classification performance across cohorts, with gains concentrated in the early weeks of the semester when current-cohort data are scarce.