Comparison of Hyperpriors for Modeling the Intertrait Correlation in a Multidimensional IRT Model

Abstract

Markov chain Monte Carlo (MCMC) algorithms have made the estimation of multidimensional item response theory (MIRT) models possible under a fully Bayesian framework. An important goal in fitting a MIRT model is to accurately estimate the interrelationship among multiple latent traits. In Bayesian hierarchical modeling, this is realized through modeling the covariance matrix, which is typically done via the use of an inverse Wishart prior distribution due to its conjugacy property. Studies in the Bayesian literature have pointed out limitations of such specifications. The purpose of this study is to compare the inverse Wishart prior with other alternatives such as the scaled inverse Wishart, the hierarchical half-t, and the LKJ priors on parameter estimation and model adequacy of one form of the MIRT model through Monte Carlo simulations. Results suggest that the inverse Wishart prior performs worse than the other priors on parameter recovery and model-data adequacy across most of the simulation conditions when variance for person parameters is small. Findings from this study provide a set of guidelines on using these priors in estimating the Bayesian MIRT models.