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Extensions to Mean–Geometric Mean 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

Mean-geometric mean (MGM) linking is a widely used method for linking two groups within the two-parameter logistic (2PL) item response model. However, the presence of differential item functioning (DIF) can lead to biased parameter estimates using the traditional MGM method. To address this, alternative linking methods based on robust loss functions have been proposed. In this article, the conventional L 2 loss function is compared with the L 0.5 and L 0 loss functions in MGM linking. Our results suggest that robust loss functions are preferable when dealing with outlying DIF effects, with the L 0 function showing particular advantages in tests with larger item sets and sample sizes. Additionally, a simulation study demonstrates that defining MGM linking based on item intercepts rather than item difficulties leads to more accurate linking parameter estimates. Finally, robust Haberman linking slightly outperforms robust MGM linking in two-group comparisons.

Suggested Citation

  • Alexander Robitzsch, 2024. "Extensions to Mean–Geometric Mean Linking," Mathematics, MDPI, vol. 13(1), pages 1-14, December.
    • Handle: RePEc:gam:jmathe:v:13:y:2024:i:1:p:35-:d:1553813
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    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.
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    3. Michela Battauz, 2017. "Multiple Equating of Separate IRT Calibrations," Psychometrika, Springer;The Psychometric Society, vol. 82(3), pages 610-636, September.
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    5. Peter F. Halpin, 2024. "Differential Item Functioning via Robust Scaling," Psychometrika, Springer;The Psychometric Society, vol. 89(3), pages 796-821, September.
    6. Wim J. Linden & Michelle D. Barrett, 2016. "Linking Item Response Model Parameters," Psychometrika, Springer;The Psychometric Society, vol. 81(3), pages 650-673, September.
    7. Battauz, Michela, 2015. "equateIRT: An R Package for IRT Test Equating," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 68(i07).
    8. Alexander Robitzsch, 2024. "Examining Differences of Invariance Alignment in the Mplus Software and the R Package Sirt," Mathematics, MDPI, vol. 12(5), pages 1-16, March.
    Full references (including those not matched with items on IDEAS)

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