An Implementation of the Gibbs Sampling Method Under the Rasch Model

A brief explication of the implementation of the Gibbs sampling method via rejection sampling to obtain Bayesian estimates of difficulty and ability parameters under the Rasch model is presented. The Gibbs sampling method via rejection sampling was used in conjunction with the computer program OpenBUGS. Examples that compared the estimation method with another Gibbs sampling method via data augmentation as well as conditional, marginal, and joint maximum likelihood estimation methods are presented using empirical data sets. The effects of prior specifications on the difficulty and ability estimates are illustrated with the empirical data sets. A discussion is presented for related issues of Bayesian estimation in item response theory