Robust Haebara Linking for Many Groups: Performance in the Case of Uniform DIF

Abstract

The comparison of group means in item response models constitutes an important issue in empirical research. The present article discusses a slight extension of the robust Haebara linking approach of He and Cui by proposing a flexible class of robust Haebara linking functions for comparisons of many groups. These robust linking functions are robust against violations of invariance. In this article, we investigate the performance of robust Haebara linking in the presence of uniform DIF effects. In an analytical derivation, it is shown that the robust Haebara linking approach provides unbiased estimates of group means in the limiting case p=0. In a simulation study, it is demonstrated that the proposed variant of the Haebara linking approach outperforms existing implementations of Haebara linking to some extent. In an empirical application using PISA data, it is illustrated that country means can be sensitive to the choice of linking functions.