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An Item Response Model with Internal Restrictions on Item Difficulty

Published online by Cambridge University Press:  01 January 2025

René Butter ,
Paul De Boeck  and
Norman Verhelst
René Butter
Affiliation:
University of Leuven, Leuven, Belgium
Paul De Boeck*
Affiliation:
University of Leuven, Leuven, Belgium
Norman Verhelst
Affiliation:
CITO, Arnhem, The Netherlands
*
Requests for reprints should be sent to Paul De Boeck, Department of Psychology, Tiensestraat 102, B-3000 Leuven, BELGIUM. E-mail: Paul.DeBoeck@psy.kuleuven.ac.be
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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.

Keywords

item response theorycomponential modelslinear restrictions

Information

Type
Original Paper
Information
Psychometrika , Volume 63 , Issue 1 , March 1998 , pp. 47 - 63
Copyright
Copyright © 1998 The Psychometric Society

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Footnotes

We thank Eric Maris for his helpful comments.

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