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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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    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. Ke-Hai Yuan & Ying Cheng & Jeff Patton, 2014. "Information Matrices and Standard Errors for MLEs of Item Parameters in IRT," Psychometrika, Springer;The Psychometric Society, vol. 79(2), pages 232-254, April.
    3. William Meredith, 1993. "Measurement invariance, factor analysis and factorial invariance," Psychometrika, Springer;The Psychometric Society, vol. 58(4), pages 525-543, December.
    4. Xiangyi Liao & Daniel M. Bolt, 2021. "Item Characteristic Curve Asymmetry: A Better Way to Accommodate Slips and Guesses Than a Four-Parameter Model?," Journal of Educational and Behavioral Statistics, , vol. 46(6), pages 753-775, December.
    5. 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.
    6. Roy Levy, 2009. "The Rise of Markov Chain Monte Carlo Estimation for Psychometric Modeling," Journal of Probability and Statistics, Hindawi, vol. 2009, pages 1-18, December.
    7. Shelby Haberman & Sandip Sinharay & Kyong Chon, 2013. "Assessing Item Fit for Unidimensional Item Response Theory Models Using Residuals from Estimated Item Response Functions," Psychometrika, Springer;The Psychometric Society, vol. 78(3), pages 417-440, July.
    8. Stanislav Kolenikov, 2010. "Resampling variance estimation for complex survey data," Stata Journal, StataCorp LLC, vol. 10(2), pages 165-199, June.
    9. Alexander Robitzsch, 2023. "Linking Error in the 2PL Model," J, MDPI, vol. 6(1), pages 1-27, January.
    10. 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.
    11. Alexander Robitzsch, 2024. "Bias-Reduced Haebara and Stocking–Lord Linking," J, MDPI, vol. 7(3), pages 1-12, September.
    12. Paul Boeck, 2008. "Random Item IRT Models," Psychometrika, Springer;The Psychometric Society, vol. 73(4), pages 533-559, December.
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