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Estimation of Standard Error, Linking Error, and Total Error for Robust and Nonrobust Linking Methods in the Two-Parameter Logistic Model

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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

The two-parameter logistic (2PL) item response theory model is a statistical model for analyzing multivariate binary data. In this article, two groups are brought onto a common metric using the 2PL model using linking methods. The linking methods of mean–mean linking, mean–geometric–mean linking, and Haebara linking are investigated in nonrobust and robust specifications in the presence of differential item functioning (DIF). M-estimation theory is applied to derive linking errors for the studied linking methods. However, estimated linking errors are prone to sampling error in estimated item parameters, thus resulting in artificially increased the linking error estimates in finite samples. For this reason, a bias-corrected linking error estimate is proposed. The usefulness of the modified linking error estimate is demonstrated in a simulation study. It is shown that a simultaneous assessment of the standard error and linking error in a total error must be conducted to obtain valid statistical inference. In the computation of the total error, using the bias-corrected linking error estimate instead of the usually employed linking error provides more accurate coverage rates.

Suggested Citation

  • 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.
  • Handle: RePEc:gam:jstats:v:7:y:2024:i:3:p:36-612:d:1419601
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    References listed on IDEAS

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