Comparing robust Haberman linking and invariance alignment

Linking methods are widely used in the social sciences to compare group differences regarding the mean and the standard deviation of a factor variable. This article examines a comparison between robust Haberman linking (HL) and invariance alignment (IA) for factor models with dichotomous and continuous items, utilizing the 𝐿0.5 and 𝐿0 loss functions. A simulation study demonstrates that HL outperforms IA when item intercepts are used for linking, rather than the original HL approach, which relies on item difficulties. The results regarding the choice of loss function were mixed: 𝐿0 showed superior performance in the simulation study with continuous items, while 𝐿0.5 performed better in the study with dichotomous items.