A Gibbs Sampling Algorithm with Monotonicity Constraints for Diagnostic Classification Models

Diagnostic classification models (DCMs) are restricted latent class with a set of cross-class equality constraints and additional monotonicity on their item parameters, both which needed to ensure the meaning classes model parameters. In this paper, we develop an efficient, Gibbs sampling-based Bayesian Markov chain Monte Carlo estimation method for general DCMs constraints. A simulation study was conducted evaluate parameter recovery algorithm showed accurate Moreover, proposed compared previously developed sampling imposed only main effect parameters log-linear cognitive diagnosis model. The newly less bias faster convergence. An analysis 2000 Programme International Student Assessment reading assessment data using also conducted.