IDEAS home Printed from https://ideas.repec.org/a/spr/psycho/v88y2023i4d10.1007_s11336-023-09931-8.html
   My bibliography  Save this article

Estimating and Using Block Information in the Thurstonian IRT Model

Author

Listed:
  • Susanne Frick

    (University of Mannheim
    TU Dortmund University)

Abstract

Multidimensional forced-choice (MFC) tests are increasing in popularity but their construction is complex. The Thurstonian item response model (Thurstonian IRT model) is most often used to score MFC tests that contain dominance items. Currently, in a frequentist framework, information about the latent traits in the Thurstonian IRT model is computed for binary outcomes of pairwise comparisons, but this approach neglects stochastic dependencies. In this manuscript, it is shown how to estimate Fisher information on the block level. A simulation study showed that the observed and expected standard errors based on the block information were similarly accurate. When local dependencies for block sizes $$>\,2$$ > 2 were neglected, the standard errors were underestimated, except with the maximum a posteriori estimator. It is shown how the multidimensional block information can be summarized for test construction. A simulation study and an empirical application showed small differences between the block information summaries depending on the outcome considered. Thus, block information can aid the construction of reliable MFC tests.

Suggested Citation

  • Susanne Frick, 2023. "Estimating and Using Block Information in the Thurstonian IRT Model," Psychometrika, Springer;The Psychometric Society, vol. 88(4), pages 1556-1589, December.
    • Handle: RePEc:spr:psycho:v:88:y:2023:i:4:d:10.1007_s11336-023-09931-8
    DOI: 10.1007/s11336-023-09931-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11336-023-09931-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11336-023-09931-8?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. Anna Brown, 2016. "Item Response Models for Forced-Choice Questionnaires: A Common Framework," Psychometrika, Springer;The Psychometric Society, vol. 81(1), pages 135-160, March.
    2. Joris Mulder & Wim Linden, 2009. "Multidimensional Adaptive Testing with Optimal Design Criteria for Item Selection," Psychometrika, Springer;The Psychometric Society, vol. 74(2), pages 273-296, June.
    3. Albert Maydeu-Olivares, 1999. "Thurstonian modeling of ranking data via mean and covariance structure analysis," Psychometrika, Springer;The Psychometric Society, vol. 64(3), pages 325-340, September.
    Full references (including those not matched with items 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. Susanne Frick, 2022. "Modeling Faking in the Multidimensional Forced-Choice Format: The Faking Mixture Model," Psychometrika, Springer;The Psychometric Society, vol. 87(2), pages 773-794, June.
    2. Chun Wang & David J. Weiss & Zhuoran Shang, 2019. "Variable-Length Stopping Rules for Multidimensional Computerized Adaptive Testing," Psychometrika, Springer;The Psychometric Society, vol. 84(3), pages 749-771, September.
    3. Lihua Yao, 2012. "Multidimensional CAT Item Selection Methods for Domain Scores and Composite Scores: Theory and Applications," Psychometrika, Springer;The Psychometric Society, vol. 77(3), pages 495-523, July.
    4. Ping Chen & Chun Wang, 2016. "A New Online Calibration Method for Multidimensional Computerized Adaptive Testing," Psychometrika, Springer;The Psychometric Society, vol. 81(3), pages 674-701, September.
    5. Paul-Christian Bürkner, 2022. "On the Information Obtainable from Comparative Judgments," Psychometrika, Springer;The Psychometric Society, vol. 87(4), pages 1439-1472, December.
    6. Ping Chen, 2017. "A Comparative Study of Online Item Calibration Methods in Multidimensional Computerized Adaptive Testing," Journal of Educational and Behavioral Statistics, , vol. 42(5), pages 559-590, October.
    7. Chun Wang & Hua-Hua Chang, 2011. "Item Selection in Multidimensional Computerized Adaptive Testing—Gaining Information from Different Angles," Psychometrika, Springer;The Psychometric Society, vol. 76(3), pages 363-384, July.
    8. Hua-Hua Chang & Chun Wang, 2011. "M.D. RECKASE (2009) Multidimensional Item Response Theory (Statistics for Social and Behavioral Sciences)," Psychometrika, Springer;The Psychometric Society, vol. 76(3), pages 504-506, July.
    9. Qian Wu & Monique Vanerum & Anouk Agten & Andrés Christiansen & Frank Vandenabeele & Jean-Michel Rigo & Rianne Janssen, 2021. "Certainty-Based Marking on Multiple-Choice Items: Psychometrics Meets Decision Theory," Psychometrika, Springer;The Psychometric Society, vol. 86(2), pages 518-543, June.
    10. Chun Wang, 2015. "On Latent Trait Estimation in Multidimensional Compensatory Item Response Models," Psychometrika, Springer;The Psychometric Society, vol. 80(2), pages 428-449, June.
    11. Jingwen Li & Jianan Sun & Mingyu Shao & Yinghui Lai & Chen Chen, 2025. "A New Multidimensional Computerized Testing Approach: On-the-Fly Assembled Multistage Adaptive Testing Based on Multidimensional Item Response Theory," Mathematics, MDPI, vol. 13(4), pages 1-27, February.
    12. Chun Wang & Hua-Hua Chang & Keith Boughton, 2011. "Kullback–Leibler Information and Its Applications in Multi-Dimensional Adaptive Testing," Psychometrika, Springer;The Psychometric Society, vol. 76(1), pages 13-39, January.
    13. Anna Brown, 2016. "Item Response Models for Forced-Choice Questionnaires: A Common Framework," Psychometrika, Springer;The Psychometric Society, vol. 81(1), pages 135-160, March.
    14. Zhewen Fan & Chun Wang & Hua-Hua Chang & Jeffrey Douglas, 2012. "Utilizing Response Time Distributions for Item Selection in CAT," Journal of Educational and Behavioral Statistics, , vol. 37(5), pages 655-670, October.
    15. Albert Maydeu-Olivares, 2001. "Limited information estimation and testing of Thurstonian models for paired comparison data under multiple judgment sampling," Psychometrika, Springer;The Psychometric Society, vol. 66(2), pages 209-227, June.
    16. Chun Wang, 2014. "Improving Measurement Precision of Hierarchical Latent Traits Using Adaptive Testing," Journal of Educational and Behavioral Statistics, , vol. 39(6), pages 452-477, December.
    17. Hua-Hua Chang, 2015. "Psychometrics Behind Computerized Adaptive Testing," Psychometrika, Springer;The Psychometric Society, vol. 80(1), pages 1-20, March.
    18. Chalmers, R. Philip, 2016. "Generating Adaptive and Non-Adaptive Test Interfaces for Multidimensional Item Response Theory Applications," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 71(i05).
    19. Lam, K.Y. & Koning, A.J. & Franses, Ph.H.B.F., 2010. "Ranking Models in Conjoint Analysis," Econometric Institute Research Papers EI 2010-51, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    20. Hyeon-Ah Kang & Yi Zheng & Hua-Hua Chang, 2020. "Online Calibration of a Joint Model of Item Responses and Response Times in Computerized Adaptive Testing," Journal of Educational and Behavioral Statistics, , vol. 45(2), pages 175-208, April.

    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:88:y:2023:i:4:d:10.1007_s11336-023-09931-8. 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.