A MATLAB Package for Markov Chain Monte Carlo with a Multi-Unidimensional IRT Model

Abstract

Unidimensional item response theory (IRT) models are useful when each item is designed to measure some facet of a unified latent trait. In practical applications, items are not necessarily measuring the same underlying trait, and hence the more general multi-unidimensional model should be considered. This paper provides the requisite information and description of software that implements the Gibbs sampler for such models with two item parameters and a normal ogive form. The software developed is written in the MATLAB package IRTmu2no. The package is flexible enough to allow a user the choice to simulate binary response data with multiple dimensions, set the number of total or burn-in iterations, specify starting values or prior distributions for model parameters, check convergence of the Markov chain, as well as obtain Bayesian fit statistics. Illustrative examples are provided to demonstrate and validate the use of the software package.

Keywords

• multi-unidimensional IRT
• two-parameter normal ogive models
• MCMC
• Gibbs sampling
• Gelman-Rubin R
• Bayesian DIC
• posterior predictive model checks
• MATLAB