Differential item functioning among multiple groups: an outlier identification approach

Differential item functioning (DIF) has received increasing focus in the past decades. Recently, Magis and De Boeck (2010) proposed to identify differentially functioning items as outliers in a one-dimensional space of DIF measures, using robust statistical tools for outlier identification. The purpose of this talk is to present an extension of this approach for the case of more than one focal group.
In this multiple group framework, items can be characterized by multiple vectors of DIF measures, one for each focal group, so that a multivariate DIF space is obtained. DIF items can then be identified as outliers in this multivariate space, based on robust multivariate estimators of location and dispersion. The MCD (Minimum Covariance Determinant) estimator is shown to be adequate for this purpose. A major asset of the method that it can rely on existing DIF indices to define the DIF vectors, and that it does not need a purification step. Alternatively, it can be used to determine on an anchor set. The method will be illustrated by an example about calculator effects on mathematics test items.