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 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.