Conclusion

A system of five item response models for multi-method data has been presented that belongs to the family of generalized Rasch models. The basic model of this system is the most restrictive three-factor extension of the simple two-factor Rasch model. A kind of asymmetry is inherent in this system, because traditionally an interaction between items and persons has been taboo in item response theory and, in particular, in Rasch models. As a "weak" form of such an interaction, the approach of class-specific Rasch models (that is, the mixed Rasch model) has been proposed to fill this gap.

Hence, the system covers five models:

■ The main effects model

■ The items-methods interaction model

■ The methods-persons interaction model

FIGURE 18.7. Item parameter values depending on the cognitive competence for each class of the two-class model.

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