Real and Artificial Differential Item Functioning in Polytomous Items

Abstract

Differential item functioning (DIF) for an item between two groups is present if, for the same person location on a variable, persons from different groups have different expected values for their responses. Applying only to dichotomously scored items in the popular Mantel–Haenszel (MH) method for detecting DIF in which persons are classified by their total scores on an instrument, Andrich and Hagquist articulated the concept of artificial DIF and showed that as an artifact of the MH method, real DIF in one item favoring one group inevitably induces artificial DIF favoring the other group in all other items. Using the dichotomous Rasch model in which the total score for a person is a sufficient statistic, and therefore justifies classifying persons by their total scores, Andrich and Hagquist showed that to distinguish between real and artificial DIF in an item identified by the MH method, a sequential procedure for resolving items is implied. Using the polytomous Rasch model, this article generalizes the concept of artificial DIF to polytomous items, in which multiple item parameters play a role. The article shows that the same principle of resolving items sequentially as with dichotomous items applies also to distinguishing between real and artificial DIF with polytomous items. A real example and a small simulated example that parallels the real example are used illustratively.