Markov chain Monte Carlo estimation of a mixture item response theory model |
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Authors: | Sun-Joo Cho Allan S Cohen Seock-Ho Kim |
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Institution: | 1. Department of Psychology and Human Development , Vanderbilt University , Peabody Hobbs #213A, 230 Appleton Place, Nashville , TN , 37203 , USA;2. Department of Educational Psychology &3. Instructional Technology , The University of Georgia , Institute for Interdisciplinary Research on Education and Human Development and Georgia Center for Assessment, 570 Aderhold Hall, Athens , GA , 30602 , USA;4. Instructional Technology , The University of Georgia , 325 Aderhold Hall, Athens , GA , 30602 , USA |
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Abstract: | Markov chain Monte Carlo (MCMC) algorithms have been shown to be useful for estimation of complex item response theory (IRT) models. Although an MCMC algorithm can be very useful, it also requires care in use and interpretation of results. In particular, MCMC algorithms generally make extensive use of priors on model parameters. In this paper, MCMC estimation is illustrated using a simple mixture IRT model, a mixture Rasch model (MRM), to demonstrate how the algorithm operates and how results may be affected by some commonly used priors. Priors on the probabilities of mixtures, label switching, model selection, metric anchoring, and implementation of the MCMC algorithm using WinBUGS are described, and their effects illustrated on parameter recovery in practical testing situations. In addition, an example is presented in which an MRM is fitted to a set of educational test data using the MCMC algorithm and a comparison is illustrated with results from three existing maximum likelihood estimation methods. |
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Keywords: | mixture item response theory model Bayesian estimation label switching model selection use of priors |
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