Investigating a Weakly Informative Prior for Item Scale Hyperparameters in Hierarchical 3PNO IRT Models

The half-t family has been suggested for the scale hyperparameter in Bayesian hierarchical modeling. Two parameters define a half-t distribution: the scale s and the degree-of-freedom ν. When s is set at a finite value that is slightly larger than the actual standard deviation of the parameters, the half-t prior density can be vaguely informative. This paper focused on such densities, and applied them to the hierarchical three-parameter item response theory (IRT) model. Monte Carlo simulations were carried out to investigate the performance of such specifications in parameter recovery and model comparisons under situations where the actual variability of item parameters varied, and results suggest that the half-t family does offer advantages over the commonly adopted uniform or inverse-gamma prior density by allowing the variability for item parameters to be either very small or large. A real data example is also provided to further illustrate this.