Computerized Adaptive Test (CAT) Applications and Item Response Theory Models for Polytomous Items

This article aims toprovide a theoretical framework forcomputerized adaptive tests (CAT) and item response theory models forpolytomous items. Besides that, it aims to introduce the simulation and liveCAT software to the related researchers. Computerized adaptive test algorithm,assumptions of item response theory models, nominalresponse model, partial credit and generalized partial credit models and gradedresponse model are described carefully to reach that aim. Likewise, itemselection methods, such as maximum Fisher information, maximum expectedinformation, minimum expected posteriorvariance, maximum expected posterior weighted-information, and abilityprediction methods, such as expected a posteriori and maximum a posteriori, areexpounded as well as stopping rules for the computerized adaptive tests.