The mixture item response model for ability decline during testing

In a long test or a low-stakes test, examinees may lose their interests or become tired as the testing progresses. That is, examinees do not demonstrate fully their maximum ability throughout the test such that their performances decline gradually. If such effect of ability decline during testing exists but is not taken into consideration by fitting a standard IRT model, the difficulties of items presented toward the end of the test will be overestimated, and as a result, the person measures will be biased. In this study, we developed a new mixture IRT model that accounts for such effect directly. Parameter recovery was assessed through simulations. The results showed that the parameters could be recovered fairly well using WinBUGS. The simulation also demonstrated that: when test data had such effect, fitting standard IRT models would overestimate item difficulties for items presented toward the end of the test; whereas fitting the new model yielded accurate parameter estimates; when test data did not have such effect, fitting the new model yielded parameter estimates that were very similar to those obtained by fitting standard IRT models. In sum, the new model is very useful when ability declines during testing and does little harm when such effect does not exist.