Exploring the posterior of a hierarchical IRT model for item effects (Q1424600)

This paper illustrates advantages of the Bayesian approach to exploration of the item response theory (IRT) model, which is a valuable tool for analysis of responses of a group of persons to a set of items. It is shown that the model can be estimated quite straightforwardly using Bayesian estimation based on Markov Chain Monte Carlo (MCMC) methods. In particular, two versions of the Gibbs sampler, namely Metropolis-Hastings within Gibbs (MMG) and data augmented Gibbs (DAG) work well for the mentioned model. The posterior of the hierarchical IRT model is explored with respect to the location of parameters and uncertainty of these parameter estimates. The posterior correlations among parameters are shown to be due to trade-off effects among parameters either on the same parameter scale or on different parameter scales.