Simple nonparametric checks for model data fit in CAT

In this paper, the usefulness of several nonparametric checks is discussed in a computerized adaptive testing (CAT) context. Although there is no tradition of nonparametric scalability in CAT, it can be argued that scalability checks can be useful to investigate, for example, the quality of item pools. Although IRT models are strongly embedded in the development and construction of CAT, the development of CAT is strongly related to parametric as opposed to nonparametric IRT modeling. This is not surprising because one of the key features of a CAT is the item selection procedure on the basis of an estimated latent trait from a calibrated item pool. Parametric IRT models enable the separate estimation of item and person parameters and, thus, facilitate this process enormously. The recent developments in nonparametric IRT, however, also suggest that techniques and statistics used in this IRT field may contribute to the development and improvement of the psychometric quality of a CAT. Investigating nonparametric IRT modeling may also help us to gain insight into the assumptions underlying CAT and may help to unify IRT modeling.