Generalized Rasch Models for Multimethod Data

The multimethod Rasch model introduced in the previous section can be considered to be a main effects model in the terminology of analysis of variance. Because there are three factors—persons, items, and methods—in this main effects model, three first-order interactions can be distinguished: interactions between methods and items, between persons and methods, and between items and persons. The last-mentioned interaction, however, would contradict the principle of Rasch models to separate the influence of persons and items on the response behavior. Such an interaction would mean that the item parameter differs among persons, that is, the difficulty of an item would be person specific. The mixed Rasch model (Rost, 1990, 1991), which is a combination of the Rasch model with latent class analysis, allows for a very restricted type of person-item interaction by assuming that different sets of item parameters hold for different groups of persons. Therefore, the approach of mixture dis-

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