Table of Contents
ISRN Applied Mathematics
Volume 2012, Article ID 269385, 14 pages
Research Article

A Gibbs Sampler for the Multidimensional Item Response Model

Section on Statistics and Measurement, Department of EPSE, Southern Illinois University Carbondale, Wham 223, MailCode 4618, Carbondale, IL 62901-4618, USA

Received 2 March 2012; Accepted 26 March 2012

Academic Editors: S. He and X. Xue

Copyright © 2012 Yanyan Sheng and Todd C. Headrick. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Current procedures for estimating compensatory multidimensional item response theory (MIRT) models using Markov chain Monte Carlo (MCMC) techniques are inadequate in that they do not directly model the interrelationship between latent traits. This limits the implementation of the model in various applications and further prevents the development of other types of IRT models that offer advantages not realized in existing models. In view of this, an MCMC algorithm is proposed for MIRT models so that the actual latent structure is directly modeled. It is demonstrated that the algorithm performs well in modeling parameters as well as intertrait correlations and that the MIRT model can be used to explore the relative importance of a latent trait in answering each test item.