Y s

■ The methods-persons and items-methods interaction model

■ The items-methods mixed Rasch model.

Methods-persons interaction simply means assuming method-specific dimensions, that is, mul-

tidimensionality. Items-methods interaction means assuming the ordinary Rasch model for as many items as there are items-methods interactions. In this case, it is the absence of an interaction (that is, the main effects model for methods and items) that leads to an extended model structure (linear logistic models). As another kind of multidimensionality, mixture distribution models can be taken into account for modeling interactions between methods and persons.

The application of these models sometimes requires new and more flexible methods of parameter estimation, measures of accuracy, and model control than those belonging to the standard repertoire of the simple Rasch model. However, these methods do exist and can be applied to multi-method data. Other model specifications are only available in principle, but convenient software is lacking. For example, the program FACETS can be used to estimate main effects models or the program ConQuest for many kinds of multidimensional models. Currently, no program exists that provides options for the exploratory analysis of the number of dimensions needed for a given set of data. Yet there is WINMIRA (von Davier, 2001), a program that has a strong exploratory capacity with respect to the kind and number of latent classes involved in a mixture distribution.

In conclusion, we do not think that another kind of item response theory is needed for multi-method data. What we need is the intelligent application of the many existing generalized IRT models, and we need good, solid theories that guide us through the complex and sometimes confusing world of generalized models. General model structures that seem to explain everything do not really explain anything, if there is not an a priori theory.

Chapter 19

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