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Markov Chain Estimation for Test Theory Without An Answer Key

Published online by Cambridge University Press:  01 January 2025

George Karabatsos  and
William H. Batchelder
George Karabatsos*
Affiliation:
University of Illinois, Chicago
William H. Batchelder
Affiliation:
University of California, Irvine
*
Requests for reprints should be sent to George Karabatsos, University of Illinois-Chicago, College of Education, 1040 W. Haxrison Street (MC 147), Chicago, IL 60607, E-Mail: [email protected]
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Abstract

This study develops Markov Chain Monte Carlo (MCMC) estimation theory for the General Condorcet Model (GCM), an item response model for dichotomous response data which does not presume the analyst knows the correct answers to the test a priori (answer key). In addition to the answer key, respondent ability, guessing bias, and difficulty parameters are estimated. With respect to data-fit, the study compares between the possible GCM formulations, using MCMC-based methods for model assessment and model selection. Real data applications and a simulation study show that the GCM can accurately reconstruct the answer key from a small number of respondents.

Keywords

consensus theoryBayesian inferenceMarkov Chain Monte Carloposterior predictive model evaluationBayesian model selection
Type
Article
Information
Psychometrika , Volume 68 , Issue 3 , September 2003 , pp. 373 - 389
Copyright
Copyright © 2003 The Psychometric Society

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Footnotes

This study was supported in part by Spencer Foundation grant SG2001000020, George Karabatsos, Principal Investigator, and also in part by NSF Renewal Grant SES-0001550 to A.K. Romney and W.H. Batchelder, Co-Principal Investigators. The second author acknowledges the kind support of the Santa Fe Institute, where he worked on aspects of this paper as a Visiting Professor in the fall of 2001. Both authors appreciate the detailed comments offered by the Editor and two referees on an earlier version of the manuscript.

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