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

Abstract

This article aims to provide a theoretical framework for computerized adaptive tests (CAT) and item response theory models for polytomous items. Besides that, it aims to introduce the simulation and live CAT software to the related researchers. Computerized adaptive test algorithm, assumptions of item response theory models, nominal response model, partial credit and generalized partial credit models and graded response model are described carefully to reach that aim. Likewise, item selection methods, such as maximum Fisher information, maximum expected information, minimum expected posterior variance, maximum expected posterior weighted-information, and ability prediction methods, such as expected a posteriori and maximum a posteriori, are expounded as well as stopping rules for the computerized adaptive tests.