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

Abstract

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 (Polson et al., 2013) 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 avoids the Metropolis-Hastings algorithm boring adjustment the turning parameters to achieve an appropriate acceptance probability. Four simulation studies are conducted and a detailed analysis of fraction subtraction data is carried out to further illustrate the proposed methodology.