Journal of Educational Measurement vol:47 issue:4 pages:432-457
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 is
based on a Rasch model with random item difﬁculties (besides the common random
person abilities). In addition, a mixture model is assumed for the item difﬁculties
such 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 item
difﬁculties in the DIF class may differ according to the observed person groups
while 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 with
traditional procedures, like the likelihood ratio test, the Mantel-Haenszel procedure
and the standardized p-DIF procedure. In this comparison, the RIM performs better
than the other methods. Finally, the usefulness of the model is also demonstrated on
a real life data set.