Multiple matrix sampling (MMS) theory indicates how data may be gathered to most efficiently convey information about levels of attainment in a population, but standard analyses of these data require random sampling of items from a fixed pool of items. This assumption proscribes the retirement of flawed or obsolete items from the pool as well as the addition of new items if comparability of estimates over time is to be maintained. Item response theory (IRT) permits measurement on an invariant scale without requiring that items be sampled at random from a fixed population, but standard IRT procedures cannot be used with the sparse data (at the level of subjects) that characterizes the most efficient multiple matrix sampling designs. This paper considers the merger of MMS theory and IRT theory. Three approaches (subject-level model, subject-level estimates; subject-level model, group-level estimates; and group-level model, group-level estimates) by which IRT can be applied in the assessment setting are described and compared. (Author/PN)