Linking error estimation in Haberman linking

Haberman linking is a widely used method for comparing groups using the two-parameter logistic item response model. However, the traditional Haberman linking approach relies on joint item parameter estimation, which prevents the application of standard M-estimation theory for linking error calculation in the presence of differential item functioning. To address this limitation, a novel pairwise Haberman linking method is introduced. Pairwise Haberman linking aligns with Haberman linking when no items are missing but eliminates the need for joint item parameters, allowing for the use of M-estimation theory in linking error computation. Theoretical derivations and simulation studies show that pairwise Haberman linking delivers reliable statistical inferences for items and persons, particularly in terms of coverage rates. Furthermore, using a bias-corrected linking error is recommended to reduce the influence of sample size on error estimates.