IDEAS home Printed from https://ideas.repec.org/a/spr/psycho/v78y2013i1p98-115.html
   My bibliography  Save this article

Optimal and Most Exact Confidence Intervals for Person Parameters in Item Response Theory Models

Author

Listed:
  • Anna Doebler
  • Philipp Doebler
  • Heinz Holling

Abstract

The common way to calculate confidence intervals for item response theory models is to assume that the standardized maximum likelihood estimator for the person parameter θ is normally distributed. However, this approximation is often inadequate for short and medium test lengths. As a result, the coverage probabilities fall below the given level of significance in many cases; and, therefore, the corresponding intervals are no longer confidence intervals in terms of the actual definition. In the present work, confidence intervals are defined more precisely by utilizing the relationship between confidence intervals and hypothesis testing. Two approaches to confidence interval construction are explored that are optimal with respect to criteria of smallness and consistency with the standard approach. Copyright The Psychometric Society 2013

Suggested Citation

  • Anna Doebler & Philipp Doebler & Heinz Holling, 2013. "Optimal and Most Exact Confidence Intervals for Person Parameters in Item Response Theory Models," Psychometrika, Springer;The Psychometric Society, vol. 78(1), pages 98-115, January.
    • Handle: RePEc:spr:psycho:v:78:y:2013:i:1:p:98-115
    DOI: 10.1007/s11336-012-9290-4
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11336-012-9290-4
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11336-012-9290-4?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. R. Bock & Murray Aitkin, 1981. "Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm," Psychometrika, Springer;The Psychometric Society, vol. 46(4), pages 443-459, December.
    2. Karl Klauer, 1991. "Exact and best confidence intervals for the ability parameter of the Rasch model," Psychometrika, Springer;The Psychometric Society, vol. 56(3), pages 535-547, September.
    3. Frederic Lord, 1983. "Unbiased estimators of ability parameters, of their variance, and of their parallel-forms reliability," Psychometrika, Springer;The Psychometric Society, vol. 48(2), pages 233-245, 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. Martin Biehler & Heinz Holling & Philipp Doebler, 2015. "Saddlepoint Approximations of the Distribution of the Person Parameter in the Two Parameter Logistic Model," Psychometrika, Springer;The Psychometric Society, vol. 80(3), pages 665-688, September.
    2. Piero Veronese & Eugenio Melilli, 2021. "Confidence Distribution for the Ability Parameter of the Rasch Model," Psychometrika, Springer;The Psychometric Society, vol. 86(1), pages 131-166, March.
    3. Yang Liu & Jan Hannig & Abhishek Pal Majumder, 2019. "Second-Order Probability Matching Priors for the Person Parameter in Unidimensional IRT Models," Psychometrika, Springer;The Psychometric Society, vol. 84(3), pages 701-718, September.

    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. Haruhiko Ogasawara, 2012. "Asymptotic expansions for the ability estimator in item response theory," Computational Statistics, Springer, vol. 27(4), pages 661-683, December.
    2. Xiang Liu & James Yang & Hui Soo Chae & Gary Natriello, 2020. "Power Divergence Family of Statistics for Person Parameters in IRT Models," Psychometrika, Springer;The Psychometric Society, vol. 85(2), pages 502-525, June.
    3. Martin Biehler & Heinz Holling & Philipp Doebler, 2015. "Saddlepoint Approximations of the Distribution of the Person Parameter in the Two Parameter Logistic Model," Psychometrika, Springer;The Psychometric Society, vol. 80(3), pages 665-688, September.
    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. Simon Grund & Oliver Lüdtke & Alexander Robitzsch, 2021. "On the Treatment of Missing Data in Background Questionnaires in Educational Large-Scale Assessments: An Evaluation of Different Procedures," Journal of Educational and Behavioral Statistics, , vol. 46(4), pages 430-465, August.
    6. Ogasawara, Haruhiko, 2013. "Asymptotic properties of the Bayes and pseudo Bayes estimators of ability in item response theory," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 359-377.
    7. Seonghoon Kim, 2012. "A Note on the Reliability Coefficients for Item Response Model-Based Ability Estimates," Psychometrika, Springer;The Psychometric Society, vol. 77(1), pages 153-162, January.
    8. Piero Veronese & Eugenio Melilli, 2021. "Confidence Distribution for the Ability Parameter of the Rasch Model," Psychometrika, Springer;The Psychometric Society, vol. 86(1), pages 131-166, March.
    9. Xiang Liu & Zhuangzhuang Han & Matthew S. Johnson, 2018. "The UMP Exact Test and the Confidence Interval for Person Parameters in IRT Models," Psychometrika, Springer;The Psychometric Society, vol. 83(1), pages 182-202, March.
    10. Magis, David & Raîche, Gilles, 2012. "Random Generation of Response Patterns under Computerized Adaptive Testing with the R Package catR," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 48(i08).
    11. 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.
    12. Joel A. Martínez-Regalado & Cinthia Leonora Murillo-Avalos & Purificación Vicente-Galindo & Mónica Jiménez-Hernández & José Luis Vicente-Villardón, 2021. "Using HJ-Biplot and External Logistic Biplot as Machine Learning Methods for Corporate Social Responsibility Practices for Sustainable Development," Mathematics, MDPI, vol. 9(20), pages 1-16, October.
    13. Vitoratou, Silia & Ntzoufras, Ioannis & Moustaki, Irini, 2016. "Explaining the behavior of joint and marginal Monte Carlo estimators in latent variable models with independence assumptions," LSE Research Online Documents on Economics 57685, London School of Economics and Political Science, LSE Library.
    14. Michela Battauz & Ruggero Bellio, 2011. "Structural Modeling of Measurement Error in Generalized Linear Models with Rasch Measures as Covariates," Psychometrika, Springer;The Psychometric Society, vol. 76(1), pages 40-56, January.
    15. Melissa Gladstone & Gillian Lancaster & Gareth McCray & Vanessa Cavallera & Claudia R. L. Alves & Limbika Maliwichi & Muneera A. Rasheed & Tarun Dua & Magdalena Janus & Patricia Kariger, 2021. "Validation of the Infant and Young Child Development (IYCD) Indicators in Three Countries: Brazil, Malawi and Pakistan," IJERPH, MDPI, vol. 18(11), pages 1-19, June.
    16. Björn Andersson & Tao Xin, 2021. "Estimation of Latent Regression Item Response Theory Models Using a Second-Order Laplace Approximation," Journal of Educational and Behavioral Statistics, , vol. 46(2), pages 244-265, April.
    17. Norman Cliff, 1989. "Ordinal consistency and ordinal true scores," Psychometrika, Springer;The Psychometric Society, vol. 54(1), pages 75-91, March.
    18. Tim Kaiser & Luis Oberrauch & Günther Seeber, 2020. "Measuring economic competence of secondary school students in Germany," The Journal of Economic Education, Taylor & Francis Journals, vol. 51(3-4), pages 227-242, August.
    19. Eijffinger, Sylvester & Mahieu, Ronald & Raes, Louis, 2018. "Inferring hawks and doves from voting records," European Journal of Political Economy, Elsevier, vol. 51(C), pages 107-120.
    20. 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.

    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:78:y:2013:i:1:p:98-115. 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.