Bayesian estimation of the three-parameter multi-unidimensional model

Abstract

Fully Bayesian estimation has been developed for the two-parameter multi-unidimensional IRT model. The extension of the algorithm to the three-parameter multi-unidimensional model is straightforward. Earlier work on unidimensional models indicates that with an additional pseudo-chance-level parameter, three-parameter models are more complicated than two-parameter models and noninformative prior distributions for certain item parameters create problems in the convergence of the Markov chain. Monte Carlo simulations were carried out to evaluate the performance of fully Bayesian estimation for the three-parameter multi-unidimensional model. The results suggest that similar to previous findings with unidimensional models, informative priors have to be specified for item parameters to ensure convergence. However, the intertrait correlation can be correctly estimated, which makes the model practically useful.