Bayesian Transition Diagnostic Classification Models with Polya-Gamma Augmentation

Diagnostic classification models assume the existence of latent attribute profiles, the possession of which increases the probability of responding correctly to questions requiring the corresponding attributes. Through the use of longitudinally administered exams, the degree to which students are acquiring core attributes over time can be assessed. While past approaches to longitudinal diagnostic classification modeling perform inference on the overall probability of acquiring particular attributes, there is particular interest in the relationship between student progression and student covariates such as intervention effects. To address this need, we propose an integrated Bayesian model for student progression in a longitudinal diagnostic classification modeling framework. Using Pòlya-gamma augmentation with two logistic link functions, we achieve computationally efficient posterior estimation with a conditionally Gibbs sampling procedure. We show that this approach achieves accurate parameter recovery when evaluated using simulated data. We also demonstrate the method on a real-world educational testing data set.