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Bias-Corrected Fixed Item Parameter Calibration, with an Application to PISA Data

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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

Fixed item parameter calibration (FIPC) is commonly used to compare groups or countries using an item response theory model with a common set of fixed item parameters. However, FIPC has been shown to produce biased estimates of group means and standard deviations in the presence of random differential item functioning (DIF). To address this, a bias-corrected variant of FIPC, called BCFIPC, is introduced in this article. BCFIPC eliminated the bias of FIPC with only minor efficiency losses in certain simulation conditions, but substantial precision gains in many others, particularly for estimating group standard deviations. Finally, a comparison of both methods using the PISA 2006 dataset revealed relatively large differences in country means and standard deviations.

Suggested Citation

  • Alexander Robitzsch, 2025. "Bias-Corrected Fixed Item Parameter Calibration, with an Application to PISA Data," Stats, MDPI, vol. 8(2), pages 1-29, April.
    • Handle: RePEc:gam:jstats:v:8:y:2025:i:2:p:29-:d:1641536
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    References listed on IDEAS

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    7. Alexander Robitzsch, 2023. "Linking Error in the 2PL Model," J, MDPI, vol. 6(1), pages 1-27, January.
    8. Martijn G. De Jong & Jan-Benedict E. M. Steenkamp & Jean-Paul Fox, 2007. "Relaxing Measurement Invariance in Cross-National Consumer Research Using a Hierarchical IRT Model," Journal of Consumer Research, Journal of Consumer Research Inc., vol. 34(2), pages 260-278, June.
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    11. 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.
    12. Alexander Robitzsch, 2024. "Bias-Reduced Haebara and Stocking–Lord Linking," J, MDPI, vol. 7(3), pages 1-12, September.
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