Priors in Bayesian Estimation Under the Graded Response Model

The purpose of this chapter is to review various priors used in Bayesian estimation under the graded response model with clear mathematical definitions of the prior distributions. A Bayesian estimation method, Gibbs sampling, was compared with the marginal Bayesian estimation method using empirical data. The effects of the priors and their specifications on both item and ability parameter estimates are demonstrated. Issues in Bayesian estimation, use of priors in item response theory, and selection of item response theory models are discussed.