Applications and Extensions of MCMC in IRT: Multiple Item Types, Missing Data, and Rated Responses

Patz and Junker (1999) describe a general Markov chain Monte Carlo (MCMC) strategy, based on Metropolis-Hastings sampling, for Bayesian inference in complex item response theory (IRT) settings. They demonstrate the basic methodology using the two-parameter logistic (2PL) model. In this paper we exte...

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Bibliographic Details
Published inJournal of educational and behavioral statistics Vol. 24; no. 4; pp. 342 - 366
Main Authors Patz, Richard J., Junker, Brian W.
Format Journal Article
LanguageEnglish
Published 01.12.1999
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Summary:Patz and Junker (1999) describe a general Markov chain Monte Carlo (MCMC) strategy, based on Metropolis-Hastings sampling, for Bayesian inference in complex item response theory (IRT) settings. They demonstrate the basic methodology using the two-parameter logistic (2PL) model. In this paper we extend their basic MCMC methodology to address issues such as non-response, designed missingness, multiple raters, guessing behavior and partial credit (polytomous) test items. We apply the basic MCMC methodology to two examples from the National Assessment of Educational Progress 1992 Trial State Assessment in Reading: (a) a multiple item format (2PL, 3PL, and generalized partial credit) subtest with missing response data; and (b) a sequence of rated, dichotomous short-response items, using a new IRT model called the generalized linear logistic test model (GLLTM).
ISSN:1076-9986
1935-1054
DOI:10.3102/10769986024004342