Statistical tests for person misfit in computerized adaptive testing

Recently, several person-fit statistics have been proposed to detect nonfitting response patterns. This study is designed to generalize an approach followed by Klauer (1995) to an adaptive testing system using the two-parameter logistic model (2PL) as a null model. The approach developed by Klauer is described, and some difficulties in generalizing it to a computerized adaptive testing model are explored. Alternative approaches are presented, and the results of a power study and the consequences for person-fit measurement in adaptive testing situations are discussed. The first part of the simulation concerns the ability to ignore the process that causes missing data and the impact of the fact that data in adaptive testing are not observed at random. Then the power of the proposed three tests is studied. Results suggest that tests against local independence in the 2PL have little power, but that the power for testing against nonvariant abilities is relatively larger but still low.