Bayesian Hierarchical Analysis of Polychotomous Item Responses

The Bayesian hierarchical model for polychotomous item responses and the Bayesian method for inferences of the parameters in this model were proposed using the Gibbs Sampler. The model is complex but reflects psychological reality. The method was applied to 40 sets of simulated data and its efficiency in estimation was compared to other established methods. The same method was also applied to the real data, and the individual differences of the estimated competence among the subjects of the same test score could be given good interpretation.