The impact of differential discrimination on vertical equating

This paper shows the impact of differential discrimination on the results of vertical equating when the Rasch model is applied. It is shown that where there is differential discrimination, relevant items contribute information, for the purpose of vertical equating, that contains systematic error. The impact of differential item discrimination on vertical equating is examined from a theoretical perspective, and subsequently illustrated in terms of a simulation study and an empirical example. The implication of the results shown in the paper is that data should be interrogated for evidence of differential discrimination, and relevant items should be omitted in order to minimize the impact of systematic error on the results of vertical equating. In order to minimize systematic error, evidence of differential discrimination should be given precedence over evidence of most other forms of misfit. Indices such as Outfit and Infit are commonly used to diagnose misfit associated with differential discrimination. The research described in this paper also highlights a specific limitation of such indices. Accordingly, the importance of using graphical evidence to complement fit indices is emphasized.