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Linking Error in the 2PL Model

Author

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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), 24118 Kiel, Germany)

Abstract

The two-parameter logistic (2PL) item response model is likely the most frequently applied item response model for analyzing dichotomous data. Linking errors quantify the variability in means or standard deviations due to the choice of items. Previous research presented analytical work for linking errors in the one-parameter logistic model. In this article, we present linking errors for the 2PL model using the general theory of M-estimation. Linking errors are derived in the case of log-mean-mean linking for linking two groups. The performance of the newly proposed formulas is evaluated in a simulation study. Furthermore, the linking error estimation in the 2PL model is also treated in more complex settings, such as chain linking, trend estimation, fixed item parameter calibration, and concurrent calibration.

Suggested Citation

  • Alexander Robitzsch, 2023. "Linking Error in the 2PL Model," J, MDPI, vol. 6(1), pages 1-27, January.
    • Handle: RePEc:gam:jjopen:v:6:y:2023:i:1:p:5-84:d:1032852
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    References listed on IDEAS

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    Cited by:

    1. Alexander Robitzsch, 2023. "Modeling Model Misspecification in Structural Equation Models," Stats, MDPI, vol. 6(2), pages 1-17, June.
    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. "Bias-Reduced Haebara and Stocking–Lord Linking," J, MDPI, vol. 7(3), pages 1-12, September.

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