RIM: A random item mixture model to detect Differential Item Functioning

摘要

In this paper we present a new methodology for detecting differential item functioning (DIF). We introduce a DIF model, called the random item mixture (RIM), that isbased on a Rasch model with random item difficulties (besides the common randomperson abilities). In addition, a mixture model is assumed for the item difficultiessuch that the items may belong to one of two classes: a DIF or a non-DIF class.The crucial difference between the DIF class and the non-DIF class is that the itemdifficulties in the DIF class may differ according to the observed person groupswhile they are equal across the person groups for the items from the non-DIF class.Statistical inference for the RIM is carried out in a Bayesian framework. The performance of the RIM is evaluated using a simulation study in which it is compared withtraditional procedures, like the likelihood ratio test, the Mantel-Haenszel procedureand the standardized p-DIF procedure. In this comparison, the RIM performs betterthan the other methods. Finally, the usefulness of the model is also demonstrated ona real life data set.