IDEAS home Printed from https://ideas.repec.org/a/gam/jjopen/v7y2024i3p21-384d1471015.html
   My bibliography  Save this article

Bias-Reduced Haebara and Stocking–Lord Linking

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2571-8800/7/3/21/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2571-8800/7/3/21/
    Download Restriction: no
    ---><---

    References listed on IDEAS

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

    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. Alexander Robitzsch, 2025. "Comparing Robust Haberman Linking and Invariance Alignment," Stats, MDPI, vol. 8(1), pages 1-15, 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, 2024. "Extensions to Mean–Geometric Mean Linking," Mathematics, MDPI, vol. 13(1), pages 1-14, December.
    4. 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.
    5. Gabriel Wallin & Yunxiao Chen & Irini Moustaki, 2024. "DIF Analysis with Unknown Groups and Anchor Items," Psychometrika, Springer;The Psychometric Society, vol. 89(1), pages 267-295, March.
    6. Wallin, Gabriel & Chen, Yunxiao & Moustaki, Irini, 2024. "DIF analysis with unknown groups and anchor items," LSE Research Online Documents on Economics 121991, London School of Economics and Political Science, LSE Library.
    7. Alexander Robitzsch, 2025. "Bias-Corrected Fixed Item Parameter Calibration, with an Application to PISA Data," Stats, MDPI, vol. 8(2), pages 1-29, April.
    8. 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.
    9. Alberto Maydeu-Olivares & Rosa Montaño, 2013. "How Should We Assess the Fit of Rasch-Type Models? Approximating the Power of Goodness-of-Fit Statistics in Categorical Data Analysis," Psychometrika, Springer;The Psychometric Society, vol. 78(1), pages 116-133, January.
    10. Carolina Navarro & Luis Ayala & José Labeaga, 2010. "Housing deprivation and health status: evidence from Spain," Empirical Economics, Springer, vol. 38(3), pages 555-582, June.
    11. 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.
    12. Cafarelli Ryan & Rigdon Christopher J. & Rigdon Steven E., 2012. "Models for Third Down Conversion in the National Football League," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 8(3), pages 1-26, 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. Alexander Robitzsch, 2023. "Linking Error in the 2PL Model," J, MDPI, vol. 6(1), pages 1-27, January.
    17. 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.
    18. Thiel, Hendrik & Thomsen, Stephan L., 2013. "Noncognitive skills in economics: Models, measurement, and empirical evidence," Research in Economics, Elsevier, vol. 67(2), pages 189-214.
    19. Norman Cliff, 1989. "Ordinal consistency and ordinal true scores," Psychometrika, Springer;The Psychometric Society, vol. 54(1), pages 75-91, March.
    20. W. Nicewander, 1990. "A latent-trait based reliability estimate and upper bound," Psychometrika, Springer;The Psychometric Society, vol. 55(1), pages 65-74, 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:gam:jjopen:v:7:y:2024:i:3:p:21-384:d:1471015. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.