A relation between a between-item multidimensional IRT model and the mixture rasch model Authors
First Online: 10 September 2005 DOI:
Cite this article as: Rijmen, F. & De Boeck, P. Psychometrika (2005) 70: 481. doi:10.1007/s11336-002-1007-7 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 model multidimensional IRT models mixture Rasch model Saltus model
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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