Robustness of IRT observed-score equating

One of the most important aspects of equating, scaling, and linking is whether the models used are appropriate. In this chapter, some heuristic methods and a more formal model test for the evaluation of the robustness of the procedures used for equating, scaling, and linking are presented. The methods are outlined in the framework of item response theory (IRT) observed score (OS) equating of number-correct (NC) scores (Kolen & Brennan, 1995; Zeng & Kolen, 1995). The methods for the evaluation of IRT-OS-NC equating will be demonstrated using concurrent estimation of the parameters of the one-parameter logistic (1PL) model and the three-parameter logistic (3PL) model. In this procedure the parameters are estimated on a common scale by using all available data simultaneously. The data used are from the national school-leaving examinations at the end of secondary education in the Netherlands. To put the presentation into perspective, the application will be presented first.