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A Bayesian formulation for a popular conjunctive cognitive diagnosis model, the reduced reparameterized unified model (rRUM), is developed. The new Bayesian formulation of the rRUM employs a latent response data augmentation strategy that yields tractable full conditional distributions. A Gibbs sampling algorithm is described to approximate the posterior distribution of the rRUM parameters. A Monte Carlo study supports accurate parameter recovery and provides evidence that the Gibbs sampler tended to converge in fewer iterations and had a larger effective sample size than a commonly employed Metropolis–Hastings algorithm. The developed method is disseminated for applied researchers as an R package titled “rRUM.”

An Improved Strategy for Bayesian Estimation of the Reduced Reparameterized Unified Model