COMPONENTIAL IRT MODELS FOR POLYTOMOUS ITEMS

Componential IRT models for polytomous items are of particular interes t in two contexts: componential research and test development. We assu me that there are basic components, such as processes and knowledge st ructures, involved in solving cognitive tasks. In componential researc h, the subtask paradigm may be used to isolate such components in subt asks. In test development, items may be composed such that their respo nse alternatives correspond with specific combinations of such compone nts. In both cases the data may be modeled as polytomous items. With B eck's (1972) nominal model as a general framework, transformation matr ices can be used to constrain the parameters of the response categorie s so as to reflect the componential design of the response categories. In this way, both main effects and interaction effects of components can be studied. An application to a spelling task demonstrates this ap proach.