Identification of differential item functioning in multiple-group settings: a multivariate outlier detection approach

We focus on the identification of differential item functioning (DIF) when more than two groups of examinees are considered. We propose to consider items as elements of a multivariate space, where DIF items are outlying elements. Following this approach, the situation of multiple groups is a quite natural case. A robust statistics technique is proposed to identify DIF items as outliers in the multivariate space. For low dimensionalities, up to 2-3 groups, a simple graphical tool is derived. We illustrate our approach with a reanalysis of data from Kim, Cohen, and Park (1995) on using calculators for a mathematics test.