Looking at DIF From a New Perspective: A Structure-Based Approach Acknowledging Inherent Indefinability.

Differential item functioning (DIF), although highly relevant for psychometric assessment in various fields of psychology, is mathematically not well-defined. Especially the impact, the difference between the means of the person parameters in the focal and the reference group, is a parameter that is not identified without further assumptions. Common DIF detection methods necessarily impose such assumptions, however, in most cases the specific constraints remain quite vague and are implicit in the mathematical algorithms. As an alternative, a structure-based approach is proposed that is independent of the impact and, therefore, not affected by the identification problem. The approach allows to (a) reveal all DIF-relevant information from the data, (b) define indices that quantify the amount of DIF in a test as a whole, and (c) perform item-level DIF analyses. For the last application, it is unavoidable to assume additional identification constraints. However, compared to other existing methods (which also rely on such constraints), the approach suggested here provides advantages as it is not only easier to perform but also much more transparent concerning its underlying assumptions.