, Volume 70, Issue 3, pp 481-496
Date: 10 Sep 2005

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

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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.

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.