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Multiple Equating of Separate IRT Calibrations

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  • 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
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    References listed on IDEAS

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    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.
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    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, 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.
    3. 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.
    4. Alexander Robitzsch, 2023. "Linking Error in the 2PL Model," J, MDPI, vol. 6(1), pages 1-27, January.
    5. 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.

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