Bayesian Estimation of the DINA Model With Pólya-Gamma Gibbs Sampling

摘要

With the increasing demanding for precision of test feedback, cognitive diagnosis models have attracted more and more attention to fine classify students whether has mastered some skills. The purpose of this paper is to propose a highly effective Pólya-Gamma Gibbs sampling algorithm based on auxiliary variables to estimate the deterministic inputs, noisy “and” gate model (DINA) model that have been widely used in cognitive diagnosis study. The new algorithm not only avoids the Metroplis-Hastings algorithm boring adjustment the turning parameters to achieve an appropriate acceptance probability, but also overcomes the dependence of the traditional Gibbs sampling algorithm on the conjugate prior distribution. There simulation studies are conducted and a detailed analysis of fraction subtraction data is carried out to further illustrate the proposed methodology.