Journal of educational measurement vol:32 issue:4 pages:364-384
Componential IRT models for polytomous items are of particular interest in two contexts: componential research and test development. We assume that there are basic components, such as processes and knowledge structures, involved in solving cognitive tasks. In componential research, the subtask paradigm may be used to isolate such components in subtasks. In test development, items may be composed such that their response alternatives correspond with specific combinations of such components. In both cases the data may be modeled as polytomous items. With Beck's (1972) nominal model as a general framework, transformation matrices can be used to constrain the parameters of the response categories 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 approach.