Author:

Keywords:

Gibbs Sampler, Hierarchical Modeling, IRT, Item Effects, Posterior Correlations, Science & Technology, Physical Sciences, Statistics & Probability, Mathematics, Gibbs sampler, hierarchical modeling, item effects, posterior correlations, 01 Mathematical Sciences, 08 Information and Computing Sciences, 46 Information and computing sciences, 49 Mathematical sciences

Abstract:

A one-way ANOVA structure is imposed o the item difficulty and the item discrimination parameter of a two-parameter hierarchical IRT model for item effects. Bayesian estimation of the model is illustrated for the Metropolis-Hastings within Gibbs and the data augmented Gibbs procedure. The posterior of the ierarchical IRT model is explored with respect to the location of parameters and the 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 scales or on different parameter scales.