Robust-mean-geometric-mean and Robust Haberman linking with invariant item discriminations under sparse differential item functioning

Comparison of two or multiple groups based on dichotomous items is a central task in item response theory (IRT) linking. This article considers the two-parameter logistic scaling model under sparse differential item functioning (DIF) in item intercepts and DIF-free item discriminations. Robust-mean-geometric-mean (RMGM) and robust Haberman (RHAB) linking are compared across several loss functions and under scaling models with noninvariant or invariant item discriminations. Two simulation studies show that invariant item discriminations improve the precision of estimated group means. In addition, the 𝐿0 loss function is generally preferable to the 𝐿1 and 𝐿0.5 loss functions when DIF proportions or sample sizes are large. Several empirical examples illustrate the proposed specifications.