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Bias-Reduced Haebara and Stocking–Lord Linking

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  • Alexander Robitzsch

    (IPN—Leibniz Institute for Science and Mathematics Education, Olshausenstraße 62, 24118 Kiel, Germany
    Centre for International Student Assessment (ZIB), Olshausenstraße 62, 24118 Kiel, Germany)

Abstract

Haebara and Stocking–Lord linking methods are frequently used to compare the distributions of two groups. Previous research has demonstrated that Haebara and Stocking–Lord linking can produce bias in estimated standard deviations and, to a smaller extent, in estimated means in the presence of differential item functioning (DIF). This article determines the asymptotic bias of the two linking methods for the 2PL model. A bias-reduced Haebara and bias-reduced Stocking–Lord linking method is proposed to reduce the bias due to uniform DIF effects. The performance of the new linking method is evaluated in a simulation study. In general, it turned out that Stocking–Lord linking had substantial advantages over Haebara linking in the presence of DIF effects. Moreover, bias-reduced Haebara and Stocking–Lord linking substantially reduced the bias in the estimated standard deviation.

Suggested Citation

  • Alexander Robitzsch, 2024. "Bias-Reduced Haebara and Stocking–Lord Linking," J, MDPI, vol. 7(3), pages 1-12, September.
    • Handle: RePEc:gam:jjopen:v:7:y:2024:i:3:p:21-384:d:1471015
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    References listed on IDEAS

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    1. Robin Shealy & William Stout, 1993. "A model-based standardization approach that separates true bias/DIF from group ability differences and detects test bias/DTF as well as item bias/DIF," Psychometrika, Springer;The Psychometric Society, vol. 58(2), pages 159-194, June.
    2. 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.
    3. Alexander Robitzsch, 2023. "Linking Error in the 2PL Model," J, MDPI, vol. 6(1), pages 1-27, January.
    4. Valentina Sansivieri & Marie Wiberg & Mariagiulia Matteucci, 2017. "A Review of Test Equating Methods with a Special Focus on IRT-Based Approaches," Statistica, Department of Statistics, University of Bologna, vol. 77(4), pages 329-352.
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    Cited by:

    1. Alexander Robitzsch, 2025. "Bias-Corrected Fixed Item Parameter Calibration, with an Application to PISA Data," Stats, MDPI, vol. 8(2), pages 1-29, April.

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