Robust and Nonrobust Linking of Two Groups for the Rasch Model with Balanced and Unbalanced Random DIF: A Comparative Simulation Study and the Simultaneous Assessment of Standard Errors and Linking Errors with Resampling Techniques

In this article, the Rasch model is used for assessing a mean difference between two groups test of dichotomous items. It assumed that random differential item functioning (DIF) exists can bias group differences. The case balanced DIF distinguished from unbalanced DIF. DIF, effects on average cancel out. contrast, in expected value differ zero and favor particular group. Robust linking methods (e.g., invariance alignment) aim at determining differences are robust to presence obtained nonrobust Haebara linking) be affected by few effects. Alternative compared simulation study under various conditions. turned out preferred over alternatives Moreover, theory M-estimation, as an important approach statistical estimation suitable data with asymmetric errors, asymptotic behavior estimators if number items tends infinity. These results give insights into errors represent variability estimates due selecting test. M-estimation also analytical treatment assess standard simultaneously. Finally, double jackknife half sampling introduced evaluated Half outperformed assessment methods.