Heterogeneity in IRT-Models

BMBF project, conducted at the LMU Munich

Principal investigator Prof. Dr. Carolin Strobl
Staff Dipl.-Soz. Julia Kopf, M.Sc.
Duration of the project February 1, 2011, to January 31, 2014
Funded by German Federal Ministry of Education and Research (BMBF)

The aim of this research proposal was to develop a methodological toolbox for the statistical evaluation of group-differences in complex studies in the field of competency diagnostics within the framework of Item Response Theory (IRT). The new methods will be implemented in the freely available R system for statistical computing to enable a broad applicability of the methodology in empirical educational research.

IRT includes a variety of parametric models for scaling latent traits, such as the widely-known Rasch model, which has been employed, e.g., in the PISA Study. The Rasch model ensures objective measures and fair comparisons between persons. However, this important property holds only if the underlying assumptions are met. Otherwise severe fallacies can result, e.g., in the comparison of different groups.

The methods developed in the project allow for a flexible inspection of the central assumptions and thereby provide a substantial contribution to the construction of objective and fair tests in the field of competency diagnostics.


  • Kopf, J., A. Zeileis, and C. Strobl (2014). Anchor selection strategies for DIF analysis: Review, assessment, and new approaches. Educational and Psychological Measurement. Accepted for publication.
  • Kopf, J., T. Augustin, and C. Strobl (2013). The potential of model-based recursive partitioning in the social sciences. Revisiting Ockham's Razor. In J. McArdle and G. Ritschard (Eds.), Contemporary Issues in Exploratory Data Mining, Chapter 3, pp. 75-95. Routeledge.
  • Kopf, J. (2013). Model-based recursive partitioning meets Item Response Theory. New statistical methods for the detection of Differential Item Functioning and appropriate anchor selection. Dissertation an der Fakultät für Mathematik, Informatik und Statistik. Verlag Dr. Hut.
  • Strobl, C., J. Kopf, and A. Zeileis (2013). Rasch trees: A new method for detecting differential item functioning in the Rasch model. Psychometrika. Online First.
  • Kopf, J., A. Zeileis, and C. Strobl (2013). Anchor methods for DIF detection: A comparison of the iterative forward, backward, constant and all-other anchor class. Technical Report 141.