Model-based recursive partitioning meets item response theory

The aim of this thesis is to develop new statistical methods for the evaluation of assumptions that are crucial for reliably assessing group-differences in complex studies in the field of psychological and educational testing. The framework of item response theory (IRT) includes a variety of psychometric models for scaling latent traits such as the widely-used Rasch model. The Rasch model ensures objective measures and fair comparisons between groups of subjects. However, this important property holds only if the underlying assumptions are met. One essential assumption is the invariance property. Its violation is extensively discussed in the literature and termed differential item functioning (DIF). This thesis focuses on the methodology of DIF detection. Existing methods for DIF detection are briefly discussed and new statistical methods for DIF detection are introduced together with new anchor methods. The methods introduced in this thesis allow to classify items with and without DIF more accurately and, thus, to improve the evaluation of the invariance assumption in the Rasch model. This thesis, thereby, provides a contribution to the construction of objective and fair tests in psychology and educational testing.