Psychometrika

, Volume 63, Issue 1, pp 47–63

An item response model with internal restrictions on item difficulty

Article

Abstract

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 composite tasks. A component is a generic kind of subtask of which the subtasks resulting from the decomposition are specific instantiations with respect to the particular composite tasks under study. The proposed model constrains the difficulties of the composite tasks to be linear combinations of the difficulties of the corresponding subtask items, which are estimated together with the weights used in the linear combinations, one weight for each kind of subtask. Although the model does not belong to the exponential family, its parameters can be estimated using conditional maximum likelihood estimation. The approach is demonstrated with an application to spelling tasks.

Key words

item response theory componential models linear restrictions 

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Copyright information

© The Psychometric Society 1998

Authors and Affiliations

  1. 1.University of LeuvenLeuvenBelgium
  2. 2.Department of PsychologyLeuvenBelgium
  3. 3.CitoArnhemThe Netherlands

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