Using Bayesian Methods to Identify Predictors of Freshmen Attrition

This study employs Bayesian hierarchical generalized linear models to investigate predictors of freshmen student attrition using Marist University student data from nine academic years (n=10921) and across its six schools. The proposed framework builds hierarchical binary logistic regression models to estimate the posterior probability distributions of models' parameters and derived metrics. The paper shows how to formulate hierarchical generalized (Bernoulli) linear models and implement them in a probabilistic programming platform to compute the models' parameters posterior distributions using Markov chain Monte Carlo (MCMC) techniques. Tests were carried out to study model fitness, parameter convergence and the significance of the regression parameter estimates.The results identify university academic performance, financial need, gender, and work-study program participation as predictors having a significant effect on the log-odds of freshmen attrition. Additionally, the study reveals fluctuations across time and schools. Such fluctuations would have been overlooked if flat, pooled regression models were used instead of the multilevel approach applied in this work. Variation of freshmen retention across schools highlights the need for retention-focused initiatives that include targeted strategies, as some schools seem to be more vulnerable to higher attrition rates than others. The research provides valuable findings to stakeholders, administrators, and decision-makers that can be applied and utilized by other institutions, as well as a detailed guideline on how to analyze educational data using Bayesian methods.