The article studies the problem of developing a Bayesian model formulation of the deterministic inputs, noisy “and” gate model, referred to as DINA model. After introducing the DINA model, the benefits of the proposed Bayesian formulation in the context of prior research are discussed. Then the Bayesian model formulation and full conditional distributions that are used to estimate person (i.e., latent skill/attribute profiles) and item parameters (i.e., slipping and guessing) are presented in detail. In this regard, the Markov Chain Monte Carlo (MCMC) simulation with Gibbs sampling is used. In fact, the Gibbs sampling is employed to simulate from the joint posterior distribution of item guessing and slipping parameters, subject attribute parameters, and latent class probabilities. Extension of the concepts is also provided for estimating the guessing and slipping parameters in the three- and four-parameter normal-ogive models. The ability of the proposed model to recover parameters is demonstrated in a simulation study and the results are discussed in detail. A real time application of the model using responses to a mental rotation test is given.
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