Published in the American Journal of Mathematics and Statistics, 2013, Vol. 3, No. 5, pp. 281-287. doi:10.5923/j.ajms.20130305.05


Fully Bayesian estimation has been developed for unidimensional IRT models. In this context, prior distributions can be specified in a hierarchical manner so that item hyperparameters are unknown and yet still have their own priors. This type of hierarchical modeling is useful in terms of the three-parameter IRT model as it reduces the difficulty of specifying model hyperparameters that lead to adequate prior distributions. Further, hierarchical modeling ameliorates the noncovergence problem associated with nonhierarchical models when appropriate prior information is not available. As such, a Fortran subroutine is provided to implement a hierarchical modeling procedure associated with the three-parameter normal ogive model for binary item response data using Gibbs sampling. Model parameters can be estimated with the choice of noninformative and conjugate prior distributions for the hyperparameters.