Bayesian Estimation of MIRT Models with General and Specific Latent Traits in MATLAB

Abstract

Multidimensional item response models have been developed to incorporate a general trait and several specific trait dimensions. Depending on the structure of these latent traits, different models can be considered. This paper provides the requisite information and description of software that implement the Gibbs sampling procedures for three such models with a normal ogive form. The software developed is written in the MATLAB package IRTm2noHA. The package is flexible enough to allow a user the choice to simulate binary response data with a latent structure involving general and specific traits, specify prior distributions for model parameters, check convergence of the MCMC chain, and obtain Bayesian fit statistics. Illustrative examples are provided to demonstrate and validate the use of the software package.

Keywords

• IRT
• two-parameter normal ogive models
• hierarchical structure
• additive structure
• MCMC
• Gibbs sampling
• Gelman-Rubin R
• Bayesian DIC
• posterior predictive model checks