This Article Full Text (PDF) References Alert me when this article is cited Alert me if a correction is posted Citation Map Services Email this article to a friend Similar articles in this journal Alert me to new issues of the journal Add to Saved Citations Download to citation manager Request Permissions Request Reprints Add to My Marked Citations Citing Articles Citing Articles via HighWire Citing Articles via Google Scholar Citing Articles via Scopus Google Scholar Articles by Patz, R. J. Articles by Junker, B. W. Search for Related Content Social Bookmarking                         What's this?

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

CTB/McGraw-Hill

Brian W. Junker

Carnegie Mellon University

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).

Key Words: Item response theory • Markov chain Monte Carlo • National Assessment of Educational Progress • missing data • partial credit models

Journal of Educational and Behavioral Statistics, Vol. 24, No. 4, 342-366 (1999)
DOI: 10.3102/10769986024004342


CiteULike    Complore    Connotea    Del.icio.us    Digg    Reddit    Technorati    Twitter    What's this?

This article has been cited by other articles:

				J. de la Torre and H. Song Simultaneous Estimation of Overall and Domain Abilities: A Higher-Order IRT Model Approach Applied Psychological Measurement, November 1, 2009; 33(8): 620 - 639. [Abstract] [PDF]

				J. de la Torre Improving the Quality of Ability Estimates Through Multidimensional Scoring and Incorporation of Ancillary Variables Applied Psychological Measurement, September 1, 2009; 33(6): 465 - 485. [Abstract] [PDF]

				T. M. Soares, F. B. Goncalves, and D. Gamerman An Integrated Bayesian Model for DIF Analysis Journal of Educational and Behavioral Statistics, September 1, 2009; 34(3): 348 - 377. [Abstract] [Full Text] [PDF]

				J.-P. Fox and C. Wyrick A Mixed Effects Randomized Item Response Model Journal of Educational and Behavioral Statistics, December 1, 2008; 33(4): 389 - 415. [Abstract] [Full Text] [PDF]

				J.-P. Fox and R. R. Meijer Using Item Response Theory to Obtain Individual Information From Randomized Response Data: An Application Using Cheating Data Applied Psychological Measurement, November 1, 2008; 32(8): 595 - 610. [Abstract] [PDF]

				Y. Liu, E. M. Schulz, and L. Yu Standard Error Estimation of 3PL IRT True Score Equating With an MCMC Method Journal of Educational and Behavioral Statistics, September 1, 2008; 33(3): 257 - 278. [Abstract] [Full Text] [PDF]

				J. de la Torre Multidimensional Scoring of Abilities: The Ordered Polytomous Response Case Applied Psychological Measurement, July 1, 2008; 32(5): 355 - 370. [Abstract] [PDF]

				L. T. Mariano and B. W. Junker Covariates of the Rating Process in Hierarchical Models for Multiple Ratings of Test Items Journal of Educational and Behavioral Statistics, September 1, 2007; 32(3): 287 - 314. [Abstract] [Full Text] [PDF]

				W.-C. Wang and C.-Y. Liu Formulation and Application of the Generalized Multilevel Facets Model Educational and Psychological Measurement, August 1, 2007; 67(4): 583 - 605. [Abstract] [PDF]

				T. Kang and A. S. Cohen IRT Model Selection Methods for Dichotomous Items Applied Psychological Measurement, July 1, 2007; 31(4): 331 - 358. [Abstract] [PDF]

				J. de la Torre and R. J. Patz Making the Most of What We Have: A Practical Application of Multidimensional Item Response Theory in Test Scoring Journal of Educational and Behavioral Statistics, January 1, 2005; 30(3): 295 - 311. [Abstract] [PDF]

				S. Sinharay Experiences With Markov Chain Monte Carlo Convergence Assessment in Two Psychometric Examples Journal of Educational and Behavioral Statistics, January 1, 2004; 29(4): 461 - 488. [Abstract] [PDF]

				M. S. Johnson and B. W. Junker Using Data Augmentation and Markov Chain Monte Carlo for the Estimation of Unfolding Response Models Journal of Educational and Behavioral Statistics, January 1, 2003; 28(3): 195 - 230. [Abstract] [PDF]

				S. Sinharay, M. S. Johnson, and D. M. Williamson Calibrating Item Families and Summarizing the Results Using Family Expected Response Functions Journal of Educational and Behavioral Statistics, January 1, 2003; 28(4): 295 - 313. [Abstract] [PDF]

				M. Seltzer, J. Novak, K. Choi, and N. Lim Sensitivity Analysis for Hierarchical Models Employing t Level-1 Assumptions Journal of Educational and Behavioral Statistics, January 1, 2002; 27(2): 181 - 222. [Abstract] [PDF]

				K. S. Maier Modeling Incomplete Scaled Questionnaire Data with a Partial Credit Hierarchical Measurement Model Journal of Educational and Behavioral Statistics, January 1, 2002; 27(3): 271 - 289. [Abstract] [PDF]

				R. J. Patz, B. W. Junker, M. S. Johnson, and L. T. Mariano The Hierarchical Rater Model for Rated Test Items and its Application to Large-Scale Educational Assessment Data Journal of Educational and Behavioral Statistics, January 1, 2002; 27(4): 341 - 384. [Abstract] [PDF]

				D. M. Bolt, A. S. Cohen, and J. A. Wollack A Mixture Item Response Model for Multiple-Choice Data Journal of Educational and Behavioral Statistics, January 1, 2001; 26(4): 381 - 409. [Abstract] [PDF]