Item Response Models for Grouped Data

The most familiar models of item response theory (IRT) are defined at the level of individual subjects; the form and the parameters of a model specify the probability of a correct response to a particular item from a particular subject. It is possible, however, to define an item response model at the level of salient groups of subjects; the form and the parameters of such a model would specify the probability of a correct response to a particular item from a subject selected at random from a particular group of subjects. So-called “group level†models extend the machinery of IRT to data gathered in the maximally efficient multiple-matrix sampling design, under which each sampled subject is administered only one item from a scale. This paper discusses group-level item response models, their uses, their relationships to subject-level item response models, and the estimation of model parameters.