Groups of persons and groups of items in nonparametric item response theory

In standard applications of Item Response Theory (IRT), n exchangeable persons have responded to k exchangeable items. Among neither persons nor items subgroups are distinguished This paper reviews methods and results for situations where it is meaningful to consider subgroups (of persons, of items, or both). It does so in the class of nonparametric IRT models, which is briefly explained in the first section. The main reason for such considerations is that IRT, explicitly or implicitly, not only aims to explain why certain person-item combinations have led to a positive or negative answer, but also to predict what a given person would do on other items not actually presented (test equating problems, parallel versions), and how other persons would perform on the given items (optimal test design, inference from sample to population).