UCLA

Diagnostic Classification Models (DCM) are a class of models popular in the social sciences such as Education that can be used to measure the unobservable attributes of students over multiple time points. Hidden Markov Diagnostic Classification Models (HMDCM) are an implementation of DCMs using Hidden Markov Models (HMM). The HMDCM from Yamaguchi and Martinez (2021) is a special case of HMMs where the observable and hidden states are assumed to be binary, and the models for the transition probabilities, emissions probabilities, and initial hidden state probabilities are Multinomial-Dirichlet Bayesian models. In this paper, we propose a modification to this HMDCM and introduce a Bayesian Logistic Regression Model for the emissions probabilities, where the independent variables of the logistic regression model are the hidden states and observable covariates. Our model requires that all time points have the same items, but our model omits the need for a design matrix. We adapt the VB algorithm from Yamaguchi and Martinez (2021) for this modified model, and we show, using simulations, that the algorithm can recover the true parameters with reasonable accuracy.