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Hierarchical Bayesian Modeling for Test Theory Without an Answer Key

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  • Zita Oravecz
  • Royce Anders
  • William Batchelder

Abstract

Cultural Consensus Theory (CCT) models have been applied extensively across research domains in the social and behavioral sciences in order to explore shared knowledge and beliefs. CCT models operate on response data, in which the answer key is latent. The current paper develops methods to enhance the application of these models by developing the appropriate specifications for hierarchical Bayesian inference. A primary contribution is the methodology for integrating the use of covariates into CCT models. More specifically, both person- and item-related parameters are introduced as random effects that can respectively account for patterns of inter-individual and inter-item variability. Copyright The Psychometric Society 2015

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  • Zita Oravecz & Royce Anders & William Batchelder, 2015. "Hierarchical Bayesian Modeling for Test Theory Without an Answer Key," Psychometrika, Springer;The Psychometric Society, vol. 80(2), pages 341-364, June.
    • Handle: RePEc:spr:psycho:v:80:y:2015:i:2:p:341-364
    DOI: 10.1007/s11336-013-9379-4
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    References listed on IDEAS

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    1. David Bimler, 2013. "Two applications of the Points-of-View model to subject variations in sorting data," Quality & Quantity: International Journal of Methodology, Springer, vol. 47(2), pages 775-790, February.
    2. William Batchelder & A. Romney, 1988. "Test theory without an answer key," Psychometrika, Springer;The Psychometric Society, vol. 53(1), pages 71-92, March.
    3. Paul Boeck, 2008. "Random Item IRT Models," Psychometrika, Springer;The Psychometric Society, vol. 73(4), pages 533-559, December.
    4. George Karabatsos & William Batchelder, 2003. "Markov chain estimation for test theory without an answer key," Psychometrika, Springer;The Psychometric Society, vol. 68(3), pages 373-389, September.
    5. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    6. Karl Klauer, 2010. "Hierarchical Multinomial Processing Tree Models: A Latent-Trait Approach," Psychometrika, Springer;The Psychometric Society, vol. 75(1), pages 70-98, March.
    7. Dipak Dey & Alan Gelfand & Tim Swartz & Pantelis Vlachos, 1998. "A simulation-intensive approach for checking hierarchical models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 7(2), pages 325-346, December.
    8. Miller, Elizabeth M., 2011. "Maternal health and knowledge and infant health outcomes in the Ariaal people of northern Kenya," Social Science & Medicine, Elsevier, vol. 73(8), pages 1266-1274.
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    Cited by:

    1. Florian Wickelmaier & Achim Zeileis, 2016. "Using Recursive Partitioning to Account for Parameter Heterogeneity in Multinomial Processing Tree Models," Working Papers 2016-26, Faculty of Economics and Statistics, Universität Innsbruck.
    2. repec:cup:judgdm:v:13:y:2018:i:6:p:622-635 is not listed on IDEAS
    3. Michael D. Lee, 2018. "Bayesian methods for analyzing true-and-error models," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 13(6), pages 622-635, November.

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