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

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  • Sheng, Yanyan

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.

Suggested Citation

  • Sheng, Yanyan, 2008. "A MATLAB Package for Markov Chain Monte Carlo with a Multi-Unidimensional IRT Model," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 28(i10).
    • Handle: RePEc:jss:jstsof:v:028:i10
    DOI: http://hdl.handle.net/10.18637/jss.v028.i10
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    References listed on IDEAS

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    1. R. Bock & Murray Aitkin, 1981. "Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm," Psychometrika, Springer;The Psychometric Society, vol. 46(4), pages 443-459, December.
    2. Sheng, Yanyan, 2008. "Markov Chain Monte Carlo Estimation of Normal Ogive IRT Models in MATLAB," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 25(i08).
    3. Sinharay S. & Stern H.S., 2002. "On the Sensitivity of Bayes Factors to the Prior Distributions," The American Statistician, American Statistical Association, vol. 56, pages 196-201, August.
    4. Bafumi, Joseph & Gelman, Andrew & Park, David K. & Kaplan, Noah, 2005. "Practical Issues in Implementing and Understanding Bayesian Ideal Point Estimation," Political Analysis, Cambridge University Press, vol. 13(2), pages 171-187, April.
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    Cited by:

    1. Wu, Jianmin & Bentler, Peter M., 2013. "Limited information estimation in binary factor analysis: A review and extension," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 392-403.

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