Bias and Linking Error in Fixed Item Parameter Calibration
The two-parameter logistic (2PL) item response theory (IRT) model is frequently applied to analyze group differences for multivariate binary random variables. The item parameters in the 2PL model are frequently fixed when estimating the mean and the standard deviation for a group of interest. This m...
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2024-09-01
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| author | Alexander Robitzsch |
| author_facet | Alexander Robitzsch |
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| description | The two-parameter logistic (2PL) item response theory (IRT) model is frequently applied to analyze group differences for multivariate binary random variables. The item parameters in the 2PL model are frequently fixed when estimating the mean and the standard deviation for a group of interest. This method is also called fixed item parameter calibration (FIPC). In this article, the bias and the linking error of the FIPC approach are analytically derived in the presence of random uniform differential item functioning (DIF). The adequacy of the analytical findings was validated in a simulation study. It turned out that the extent of the bias and the variance in distribution parameters increases with increasing variance of random DIF effects. |
| format | Article |
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| institution | OA Journals |
| issn | 2673-9909 |
| language | English |
| publishDate | 2024-09-01 |
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| series | AppliedMath |
| spelling | doaj-art-d71f0fe39be64647965a931362930f9d2025-08-20T01:55:57ZengMDPI AGAppliedMath2673-99092024-09-01431181119110.3390/appliedmath4030063Bias and Linking Error in Fixed Item Parameter CalibrationAlexander Robitzsch0IPN—Leibniz Institute for Science and Mathematics Education, Olshausenstraße 62, 24118 Kiel, GermanyThe two-parameter logistic (2PL) item response theory (IRT) model is frequently applied to analyze group differences for multivariate binary random variables. The item parameters in the 2PL model are frequently fixed when estimating the mean and the standard deviation for a group of interest. This method is also called fixed item parameter calibration (FIPC). In this article, the bias and the linking error of the FIPC approach are analytically derived in the presence of random uniform differential item functioning (DIF). The adequacy of the analytical findings was validated in a simulation study. It turned out that the extent of the bias and the variance in distribution parameters increases with increasing variance of random DIF effects.https://www.mdpi.com/2673-9909/4/3/63item response theory2PL modelbiaslinking errorfixed item parameter calibrationdifferential item functioning |
| spellingShingle | Alexander Robitzsch Bias and Linking Error in Fixed Item Parameter Calibration AppliedMath item response theory 2PL model bias linking error fixed item parameter calibration differential item functioning |
| title | Bias and Linking Error in Fixed Item Parameter Calibration |
| title_full | Bias and Linking Error in Fixed Item Parameter Calibration |
| title_fullStr | Bias and Linking Error in Fixed Item Parameter Calibration |
| title_full_unstemmed | Bias and Linking Error in Fixed Item Parameter Calibration |
| title_short | Bias and Linking Error in Fixed Item Parameter Calibration |
| title_sort | bias and linking error in fixed item parameter calibration |
| topic | item response theory 2PL model bias linking error fixed item parameter calibration differential item functioning |
| url | https://www.mdpi.com/2673-9909/4/3/63 |
| work_keys_str_mv | AT alexanderrobitzsch biasandlinkingerrorinfixeditemparametercalibration |