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A Relation Between a Between-Item Multidimensional IRT Model and the Mixture Rasch Model

Published online by Cambridge University Press:  01 January 2025

Frank Rijmen  and
Paul De Boeck
Frank Rijmen*
Affiliation:
Univesity of Leuven
Paul De Boeck
Affiliation:
Univesity of Leuven
*
Requests for reprints should be sent to Frank Rijmen, Department of Psychology, Univesity of Leuven, Tiensestraat 102, B-3000 Leuven, Belgium. E-mail: frank.rijmen@psy.kuleuven.ac.be
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Abstract

Two generalizations of the Rasch model are compared: the between-item multidimensional model (Adams, Wilson, and Wang, 1997), and the mixture Rasch model (Mislevy & Verhelst, 1990; Rost, 1990). It is shown that the between-item multidimensional model is formally equivalent with a continuous mixture of Rasch models for which, within each class of the mixture, the item parameters are equal to the item parameters of the multidimensional model up to a shift parameter that is specific for the dimension an item belongs to in the multidimensional model. In a simulation study, the relation between both types of models also holds when the number of classes of the mixture is as small as two. The relation is illustrated with a study on verbal aggression.

Keywords

Rasch modelmultidimensional IRT modelsmixture Rasch modelSaltus model
Type
Original Paper
Information
Psychometrika , Volume 70 , Issue 3 , September 2005 , pp. 481 - 496
Copyright
Copyright © 2005 The Psychometric Society

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Footnotes

Frank Rijmen was supported by the Fund for Scientific Research Flanders (FWO). This research is also funded by the GOA/2000/02 granted from the KU Leuven.

We would like to thank Kristof Vansteelandt for providing the data of the study on verbal aggression.

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