, Volume 68, Issue 3, pp 373–389

Markov chain estimation for test theory without an answer key


DOI: 10.1007/BF02294733

Cite this article as:
Karabatsos, G. & Batchelder, W.H. Psychometrika (2003) 68: 373. doi:10.1007/BF02294733


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.

Key words

consensus theoryBayesian inferenceMarkov Chain Monte Carloposterior predictive model evaluationBayesian model selection

Copyright information

© The Psychometric Society 2003

Authors and Affiliations

  1. 1.University of Illinois-Chicago, College of EducationChicago
  2. 2.University of California, IrvineUSA