Designing the test booklets for Rasch model calibration in a large-scale assessment with reference to numerous moderator variables and several ability dimensions

In large-scale assessments, it usually does not occur that every item of the
applicable item pool is administered to every examinee. Within item response
theory (IRT), in particular the Rasch model (1960), this is not really a problem
because item calibration works nevertheless. The different test booklets only need
to be conceptualized according to a connected incomplete block design. Yet,
connectedness of such a design should best be fulfilled severalfold, since deletion
of some items in the course of the item pool’s IRT calibration may become
necessary. The real challenge, however, is to meet constraints determined by
numerous moderator variables such as different response formats and several
topics of content – all the more so, if several ability dimensions are under
consideration, the testing duration is strongly limited or individual scoring and
feedback is an issue. In this article, we offer a report of how to deal with the
resulting problems. Experience is based on the governmental project of the
Austrian Educational Standards (Kubinger et al., 2007).