Summary

Today, important educational achievement studies, particularly large-scale assessments, use item response theory (IRT) as the method for their analyses. An important and basic assumption of IRT is on the dimensionality of a test: In order to be interpreted unidimensionally a test has to be unidimensional and hence cannot be multidimensional. Although, this basic assumption is very often neglected. The Program for International Student Assessment (PISA), for example, applies a unidimensional IRT-Model for the analysis of the mathematics achievement and at the same time applies a multidimensional IRT-model for the analysis of the four subscales of mathematics. This contradiction to one of the basic assumptions of IRT is not unique to PISA. This work, at first, discusses the currently used approaches, and presents a new approach: the generalized subdimension model (GSM). It allows the calculation of a weighted mean score within the IRT framework. The model's characteristics are compared to those of other models, particularly hierarchical models. Beyond the comparison of model fit, that is, the reliability of the results, the discussion particularly focuses on the difference in their interpretation, that is, on their validity.