An Empirical Investigation of Bayesian Hierarchical Modeling with Unidimensional IRT Models

Assuming specific values for item hyperparameters, Bayesian nonhierarchical modeling for unidimensional IRT models suffers from problems in that it relies on the availability of appropriate prior information for the three-parameter model or for small datasets. These problems can be resolved by specifying priors in a hierarchical fashion so that the item hyperparameters are unknown and have their own prior distributions. This study investigated the performance of such hierarchical modeling by comparing it with the nonhierarchical approach using Monte Carlo simulations. Their results provided empirical evidence for the advantage of using hierarchical priors in modeling unidimensional item response data when appropriate prior information is not readily available and when datasets are not sufficiently large.