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DIF Analysis with Unknown Groups and Anchor Items

The validity of instruments such as survey questionnaires or educational tests relies on a measurement invariance assumption. Essentially, regardless of group membership, responses should only reflect the latent construct the instrument measures. At the item level, a violation of this assumption is known as differential item functioning (DIF). DIF occurs when respondents sharing the same latent construct level but coming from different subgroups (defined by attributes like gender or socioeconomic status), exhibit different probabilities of responding in a specific item category. Traditional DIF analysis methods rely on knowing the comparison groups and a subset of non-DIF items. In recent years, more realistic methods have been proposed that require only one piece of information to be known. However, no method has addressed the case where both pieces of information are unknown, although such situations commonly occur in real life. This presentation introduces a DIF analysis framework that fills the gap. In the proposed method, we model the unknown groups as latent classes in a hybrid latent factor model, where item-specific DIF parameters are introduced to capture the DIF effects. Assuming that the number of DIF items is relatively small, we propose an L1-regularised estimator, designed to simultaneously identify both the latent classes and the DIF items. A computationally efficient EM algorithm is developed to solve the non-smooth optimisation problem for the regularised estimator. The performance of the proposed method is evaluated by simulation studies and an application to item response data from a real-world educational test.