IDEAS home Printed from https://ideas.repec.org/a/sae/jedbes/v45y2020i1p58-85.html
   My bibliography  Save this article

A Fast and Simple Algorithm for Bayesian Adaptive Testing

Author

Listed:
  • Wim J. van der Linden

    (University of Twente)

  • Hao Ren

    (Pearson)

Abstract

The Bayesian way of accounting for the effects of error in the ability and item parameters in adaptive testing is through the joint posterior distribution of all parameters. An optimized Markov chain Monte Carlo algorithm for adaptive testing is presented, which samples this distribution in real time to score the examinee’s ability and optimally select the items. Thanks to extremely rapid convergence of the Markov chain and simple posterior calculations, the algorithm is ready for use in real-world adaptive testing with running times fully comparable with algorithms that fix all parameters at point estimates during testing.

Suggested Citation

  • Wim J. van der Linden & Hao Ren, 2020. "A Fast and Simple Algorithm for Bayesian Adaptive Testing," Journal of Educational and Behavioral Statistics, , vol. 45(1), pages 58-85, February.
    • Handle: RePEc:sae:jedbes:v:45:y:2020:i:1:p:58-85
    DOI: 10.3102/1076998619858970
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.3102/1076998619858970
    Download Restriction: no
    File URL: https://libkey.io/10.3102/1076998619858970?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
    ---><---

    References listed on IDEAS

    as
    1. Robert Tsutakawa & Jane Johnson, 1990. "The effect of uncertainty of item parameter estimation on ability estimates," Psychometrika, Springer;The Psychometric Society, vol. 55(2), pages 371-390, June.
    2. Wim Linden & Hao Ren, 2015. "Optimal Bayesian Adaptive Design for Test-Item Calibration," Psychometrika, Springer;The Psychometric Society, vol. 80(2), pages 263-288, June.
    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. Wim J. van der Linden & Bingnan Jiang, 2020. "A Shadow-Test Approach to Adaptive Item Calibration," Psychometrika, Springer;The Psychometric Society, vol. 85(2), pages 301-321, June.

    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. Yinhong He & Ping Chen, 2020. "Optimal Online Calibration Designs for Item Replenishment in Adaptive Testing," Psychometrika, Springer;The Psychometric Society, vol. 85(1), pages 35-55, March.
    2. Ying Cheng & Ke-Hai Yuan, 2010. "The Impact of Fallible Item Parameter Estimates on Latent Trait Recovery," Psychometrika, Springer;The Psychometric Society, vol. 75(2), pages 280-291, June.
    3. C. Glas & Anna Dagohoy, 2007. "A Person Fit Test For Irt Models For Polytomous Items," Psychometrika, Springer;The Psychometric Society, vol. 72(2), pages 159-180, June.
    4. Ogasawara, Haruhiko, 2013. "Asymptotic cumulants of ability estimators using fallible item parameters," Journal of Multivariate Analysis, Elsevier, vol. 119(C), pages 144-162.
    5. Anders Skrondal & Sophia Rabe‐Hesketh, 2009. "Prediction in multilevel generalized linear models," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 172(3), pages 659-687, June.
    6. Ellen Bernadette Maria Elsman & Gerardus Hermanus Maria Bartholomeus van Rens & Ruth Marie Antoinette van Nispen, 2018. "Psychometric properties of a new intake questionnaire for visually impaired young adults: The Participation and Activity Inventory for Young Adults (PAI-YA)," PLOS ONE, Public Library of Science, vol. 13(8), pages 1-24, August.
    7. Ul Hassan, Mahmood & Miller, Frank, 2021. "An exchange algorithm for optimal calibration of items in computerized achievement tests," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    8. Mahmood Ul Hassan & Frank Miller, 2019. "Optimal Item Calibration for Computerized Achievement Tests," Psychometrika, Springer;The Psychometric Society, vol. 84(4), pages 1101-1128, December.
    9. Giada Spaccapanico Proietti & Mariagiulia Matteucci & Stefania Mignani & Bernard P. Veldkamp, 2024. "Chance-Constrained Automated Test Assembly," Journal of Educational and Behavioral Statistics, , vol. 49(1), pages 92-120, February.
    10. Wim J. van der Linden & Bingnan Jiang, 2020. "A Shadow-Test Approach to Adaptive Item Calibration," Psychometrika, Springer;The Psychometric Society, vol. 85(2), pages 301-321, June.
    11. Hao Ren & Wim J. van der Linden & Qi Diao, 2017. "Continuous Online Item Calibration: Parameter Recovery and Item Utilization," Psychometrika, Springer;The Psychometric Society, vol. 82(2), pages 498-522, June.
    12. Farinaz Havaei & V. Susan Dahinten, 2017. "How Well Does the CWEQ II Measure Structural Empowerment? Findings from Applying Item Response Theory," Administrative Sciences, MDPI, vol. 7(2), pages 1-20, May.
    13. Sheng, Yanyan, 2008. "Markov Chain Monte Carlo Estimation of Normal Ogive IRT Models in MATLAB," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 25(i08).
    14. Yang Liu & Ji Seung Yang, 2018. "Interval Estimation of Latent Variable Scores in Item Response Theory," Journal of Educational and Behavioral Statistics, , vol. 43(3), pages 259-285, June.
    15. Jodi M. Casabianca & Charles Lewis, 2015. "IRT Item Parameter Recovery With Marginal Maximum Likelihood Estimation Using Loglinear Smoothing Models," Journal of Educational and Behavioral Statistics, , vol. 40(6), pages 547-578, December.
    16. repec:jss:jstsof:25:i08 is not listed on IDEAS
    17. Wim Linden, 1998. "Stochastic order in dichotomous item response models for fixed, adaptive, and multidimensional tests," Psychometrika, Springer;The Psychometric Society, vol. 63(3), pages 211-226, September.
    18. Jinming Zhang, 2012. "The Impact of Variability of Item Parameter Estimators on Test Information Function," Journal of Educational and Behavioral Statistics, , vol. 37(6), pages 737-757, December.

    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:sae:jedbes:v:45:y:2020:i:1:p:58-85. 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: SAGE Publications (email available below). General contact details of provider: .

    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.