, Volume 70, Issue 3, pp 481–496

A relation between a between-item multidimensional IRT model and the mixture rasch model



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.


Rasch model multidimensional IRT models mixture Rasch model Saltus model 


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Copyright information

© The Psychometric Society 2005

Authors and Affiliations

  1. 1.Department of PsychologyUnivesity of LeuvenBelgium

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