Abstract
In this study, a fully Bayesian formulation has been proposed for the multiple-choice item version of the deterministic input noisy “AND” gate (MC-DINA) model, which represents a cognitive diagnostic model for extracting information from multiple-choice response data. In addition, a variational inference algorithm containing an empirical Bayesian estimation procedure was developed to solve heavy computational burden problems in Bayesian statistics procedure. The proposed method is as fast as the expectation–maximization algorithm because it does not require generation of random numbers (unlike the Markov chain Monte Carlo technique). Moreover, this algorithm can automatically extract optimal hyperparameters from analyzed data by maximizing the lower bound of the logarithm of the marginal likelihood function. The results of simulations showed that the proposed technique could successfully recover the true item and student parameters.
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