IDEAS home Printed from https://ideas.repec.org/a/spr/psycho/v80y2015i2p341-364.html
   My bibliography  Save this article

Hierarchical Bayesian Modeling for Test Theory Without an Answer Key

Author

Listed:
  • 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

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11336-013-9379-4
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11336-013-9379-4?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. William Batchelder & A. Romney, 1988. "Test theory without an answer key," Psychometrika, Springer;The Psychometric Society, vol. 53(1), pages 71-92, March.
    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 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.
    6. 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.
    7. Paul Boeck, 2008. "Random Item IRT Models," Psychometrika, Springer;The Psychometric Society, vol. 73(4), pages 533-559, December.
    8. Karl Klauer, 2010. "Hierarchical Multinomial Processing Tree Models: A Latent-Trait Approach," Psychometrika, Springer;The Psychometric Society, vol. 75(1), pages 70-98, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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.
    3. repec:cup:judgdm:v:13:y:2018:i:6:p:622-635 is not listed on IDEAS

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Royce Anders & William Batchelder, 2015. "Cultural Consensus Theory for the Ordinal Data Case," Psychometrika, Springer;The Psychometric Society, vol. 80(1), pages 151-181, March.
    2. Dora Matzke & Conor Dolan & William Batchelder & Eric-Jan Wagenmakers, 2015. "Bayesian Estimation of Multinomial Processing Tree Models with Heterogeneity in Participants and Items," Psychometrika, Springer;The Psychometric Society, vol. 80(1), pages 205-235, March.
    3. Hanneke Geerlings & Cees Glas & Wim Linden, 2011. "Modeling Rule-Based Item Generation," Psychometrika, Springer;The Psychometric Society, vol. 76(2), pages 337-359, April.
    4. Jean-Paul Fox & Joris Mulder & Sandip Sinharay, 2017. "Bayes Factor Covariance Testing in Item Response Models," Psychometrika, Springer;The Psychometric Society, vol. 82(4), pages 979-1006, December.
    5. Fernanda B. Rizzato & Roseli A. Leandro & Clarice G.B. Demétrio & Geert Molenberghs, 2016. "A Bayesian approach to analyse overdispersed longitudinal count data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(11), pages 2085-2109, August.
    6. Edgar C. Merkle & Daniel Furr & Sophia Rabe-Hesketh, 2019. "Bayesian Comparison of Latent Variable Models: Conditional Versus Marginal Likelihoods," Psychometrika, Springer;The Psychometric Society, vol. 84(3), pages 802-829, September.
    7. Crespi, Catherine M. & Boscardin, W. John, 2009. "Bayesian model checking for multivariate outcome data," Computational Statistics & Data Analysis, Elsevier, vol. 53(11), pages 3765-3772, September.
    8. Quentin F. Gronau & Eric-Jan Wagenmakers & Daniel W. Heck & Dora Matzke, 2019. "A Simple Method for Comparing Complex Models: Bayesian Model Comparison for Hierarchical Multinomial Processing Tree Models Using Warp-III Bridge Sampling," Psychometrika, Springer;The Psychometric Society, vol. 84(1), pages 261-284, March.
    9. Buddhavarapu, Prasad & Bansal, Prateek & Prozzi, Jorge A., 2021. "A new spatial count data model with time-varying parameters," Transportation Research Part B: Methodological, Elsevier, vol. 150(C), pages 566-586.
    10. Mumtaz, Haroon & Theodoridis, Konstantinos, 2017. "Common and country specific economic uncertainty," Journal of International Economics, Elsevier, vol. 105(C), pages 205-216.
    11. Jesse Elliott & Zemin Bai & Shu-Ching Hsieh & Shannon E Kelly & Li Chen & Becky Skidmore & Said Yousef & Carine Zheng & David J Stewart & George A Wells, 2020. "ALK inhibitors for non-small cell lung cancer: A systematic review and network meta-analysis," PLOS ONE, Public Library of Science, vol. 15(2), pages 1-18, February.
    12. Christina Leuker & Thorsten Pachur & Ralph Hertwig & Timothy J. Pleskac, 2019. "Do people exploit risk–reward structures to simplify information processing in risky choice?," Journal of the Economic Science Association, Springer;Economic Science Association, vol. 5(1), pages 76-94, August.
    13. Francois Olivier & Laval Guillaume, 2011. "Deviance Information Criteria for Model Selection in Approximate Bayesian Computation," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 10(1), pages 1-25, July.
    14. Raggi, Davide & Bordignon, Silvano, 2012. "Long memory and nonlinearities in realized volatility: A Markov switching approach," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3730-3742.
    15. Angelica Gianfreda & Francesco Ravazzolo & Luca Rossini, 2023. "Large Time‐Varying Volatility Models for Hourly Electricity Prices," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 85(3), pages 545-573, June.
    16. Rubio, F.J. & Steel, M.F.J., 2011. "Inference for grouped data with a truncated skew-Laplace distribution," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3218-3231, December.
    17. Quinn N. Lathrop & Ying Cheng, 2017. "Item Cloning Variation and the Impact on the Parameters of Response Models," Psychometrika, Springer;The Psychometric Society, vol. 82(1), pages 245-263, March.
    18. Alessandri, Piergiorgio & Mumtaz, Haroon, 2019. "Financial regimes and uncertainty shocks," Journal of Monetary Economics, Elsevier, vol. 101(C), pages 31-46.
    19. Padilla, Juan L. & Azevedo, Caio L.N. & Lachos, Victor H., 2018. "Multidimensional multiple group IRT models with skew normal latent trait distributions," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 250-268.
    20. Svetlana V. Tishkovskaya & Paul G. Blackwell, 2021. "Bayesian estimation of heterogeneous environments from animal movement data," Environmetrics, John Wiley & Sons, Ltd., vol. 32(6), September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:psycho:v:80:y:2015:i:2:p:341-364. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.