IDEAS home Printed from https://ideas.repec.org/a/spr/psycho/v82y2017i3d10.1007_s11336-016-9517-x.html
   My bibliography  Save this article

Multiple Equating of Separate IRT Calibrations

Author

Listed:
  • Michela Battauz

    (University of Udine)

Abstract

When test forms are calibrated separately, item response theory parameters are not comparable because they are expressed on different measurement scales. The equating process includes the conversion of item parameter estimates on a common scale and the determination of comparable test scores. Various statistical methods have been proposed to perform equating between two test forms. This paper provides a generalization to multiple test forms of the mean-geometric mean, the mean-mean, the Haebara, and the Stocking–Lord methods. The proposed methods estimate simultaneously the equating coefficients that permit the scale transformation of the parameters of all forms to the scale of the base form. Asymptotic standard errors of the equating coefficients are derived. A simulation study is presented to illustrate the performance of the methods.

Suggested Citation

  • Michela Battauz, 2017. "Multiple Equating of Separate IRT Calibrations," Psychometrika, Springer;The Psychometric Society, vol. 82(3), pages 610-636, September.
    • Handle: RePEc:spr:psycho:v:82:y:2017:i:3:d:10.1007_s11336-016-9517-x
    DOI: 10.1007/s11336-016-9517-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11336-016-9517-x
    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/s11336-016-9517-x?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. Seonghoon Kim & Michael J. Kolen, 2007. "Effects on Scale Linking of Different Definitions of Criterion Functions for the IRT Characteristic Curve Methods," Journal of Educational and Behavioral Statistics, , vol. 32(4), pages 371-397, December.
    3. Yi-Hsuan Lee & Shelby Haberman, 2013. "Harmonic Regression and Scale Stability," Psychometrika, Springer;The Psychometric Society, vol. 78(4), pages 815-829, October.
    4. Haruhiko Ogasawara, 2003. "Asymptotic standard errors of irt observed-score equating methods," Psychometrika, Springer;The Psychometric Society, vol. 68(2), pages 193-211, June.
    5. Battauz, Michela, 2015. "equateIRT: An R Package for IRT Test Equating," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 68(i07).
    6. Haruhiko Ogasawara, 2001. "Item Response Theory True Score Equatings and Their Standard Errors," Journal of Educational and Behavioral Statistics, , vol. 26(1), pages 31-50, March.
    7. Michela Battauz, 2013. "IRT Test Equating in Complex Linkage Plans," Psychometrika, Springer;The Psychometric Society, vol. 78(3), pages 464-480, July.
    8. Ogasawara, Haruhiko, 2000. "Asymptotic Standard Errors of IRT Equating Coefficients Using Moments," 商学討究 (Shogaku Tokyu), Otaru University of Commerce, vol. 51(1), pages 1-23.
    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. Alexander Robitzsch, 2023. "Comparing Robust Linking and Regularized Estimation for Linking Two Groups in the 1PL and 2PL Models in the Presence of Sparse Uniform Differential Item Functioning," Stats, MDPI, vol. 6(1), pages 1-17, January.
    2. Alexander Robitzsch, 2024. "Estimation of Standard Error, Linking Error, and Total Error for Robust and Nonrobust Linking Methods in the Two-Parameter Logistic Model," Stats, MDPI, vol. 7(3), pages 1-21, June.
    3. Alexander Robitzsch, 2020. "L p Loss Functions in Invariance Alignment and Haberman Linking with Few or Many Groups," Stats, MDPI, vol. 3(3), pages 1-38, August.
    4. Alexander Robitzsch & Oliver Lüdtke, 2022. "Mean Comparisons of Many Groups in the Presence of DIF: An Evaluation of Linking and Concurrent Scaling Approaches," Journal of Educational and Behavioral Statistics, , vol. 47(1), pages 36-68, February.
    5. Alexander Robitzsch, 2023. "Linking Error in the 2PL Model," J, MDPI, vol. 6(1), pages 1-27, January.
    6. Michela Battauz, 2023. "Testing for differences in chain equating," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 77(2), pages 134-145, May.

    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. Michela Battauz, 2023. "Testing for differences in chain equating," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 77(2), pages 134-145, May.
    2. Björn Andersson & Marie Wiberg, 2017. "Item Response Theory Observed-Score Kernel Equating," Psychometrika, Springer;The Psychometric Society, vol. 82(1), pages 48-66, March.
    3. Alexander Robitzsch, 2024. "Estimation of Standard Error, Linking Error, and Total Error for Robust and Nonrobust Linking Methods in the Two-Parameter Logistic Model," Stats, MDPI, vol. 7(3), pages 1-21, June.
    4. Michela Battauz, 2019. "On Wald tests for differential item functioning detection," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(1), pages 103-118, March.
    5. Michela Battauz, 2013. "IRT Test Equating in Complex Linkage Plans," Psychometrika, Springer;The Psychometric Society, vol. 78(3), pages 464-480, July.
    6. Michela Battauz, 2015. "Factors affecting the variability of IRT equating coefficients," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(2), pages 85-101, May.
    7. Ogasawara, Haruhiko, 2010. "Asymptotic expansions for the pivots using log-likelihood derivatives with an application in item response theory," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2149-2167, October.
    8. Haruhiko Ogasawara, 2003. "Asymptotic standard errors of irt observed-score equating methods," Psychometrika, Springer;The Psychometric Society, vol. 68(2), pages 193-211, June.
    9. Michelle D. Barrett & Wim J. van der Linden, 2019. "Estimating Linking Functions for Response Model Parameters," Journal of Educational and Behavioral Statistics, , vol. 44(2), pages 180-209, April.
    10. John Patrick Lalor & Pedro Rodriguez, 2023. "py-irt : A Scalable Item Response Theory Library for Python," INFORMS Journal on Computing, INFORMS, vol. 35(1), pages 5-13, January.
    11. Alexander Robitzsch, 2023. "Linking Error in the 2PL Model," J, MDPI, vol. 6(1), pages 1-27, January.
    12. Battauz, Michela, 2015. "equateIRT: An R Package for IRT Test Equating," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 68(i07).
    13. 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.
    14. Alexander Robitzsch, 2024. "Bias-Reduced Haebara and Stocking–Lord Linking," J, MDPI, vol. 7(3), pages 1-12, September.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    20. Norman Cliff, 1989. "Ordinal consistency and ordinal true scores," Psychometrika, Springer;The Psychometric Society, vol. 54(1), pages 75-91, March.

    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:82:y:2017:i:3:d:10.1007_s11336-016-9517-x. 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.