AN ITEM RESPONSE MODEL WITH INTERNAL RESTRICTIONS ON ITEM DIFFICULTY

An IRT model based on the Rasch model is proposed for composite tasks, that is, tasks that are decomposed into subtasks of different kinds. There is one subtask for each component that is discerned in the compo site tasks. A component is a generic kind of subtask of which the subt asks resulting from the decomposition are specific instantiations with respect to the particular composite tasks under study. The proposed m odel constrains the difficulties of the composite tasks to be linear c ombinations of the difficulties of the corresponding subtask items, wh ich are estimated together with the weights used in the linear combina tions, one weight for each kind of subtask. Although the model does no t belong to the exponential family, its parameters can be estimated us ing conditional maximum likelihood estimation. The approach is demonst rated with an application to spelling tasks.