Comparing Robust Haberman Linking and Invariance Alignment

Alexander Robitzsch ()
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Alexander Robitzsch: IPN—Leibniz Institute for Science and Mathematics Education, Olshausenstraße 62, 24118 Kiel, Germany

Stats, 2025, vol. 8, issue 1, 1-15

Abstract: 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 L 0.5 and L 0 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: L 0 showed superior performance in the simulation study with continuous items, while L 0.5 performed better in the study with dichotomous items.

Keywords: linking; Haberman linking; invariance alignment; factor model; differential item functioning; item response model; L p loss function; L 0 loss function (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2025
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