Measurement invariance across items is key to the validity of instruments like a survey questionnaire or an educational test. Differential item functioning (DIF) analysis is typically conducted to assess measurement invariance at the item level. Traditional DIF analysis methods require knowing the comparison groups (reference and focal groups) and anchor items (a subset of DIF-free items). Such prior knowledge may not always be available, and psychometric methods have been proposed for DIF analysis when one piece of information is unknown. More specifically, when the comparison groups are unknown while anchor items are known, latent DIF analysis methods have been proposed that estimate the unknown groups by latent classes. When anchor items are unknown while comparison groups are known, methods have also been proposed, typically under a sparsity assumption - the number of DIF items is not too large. However, there does not exist a method for DIF analysis when both pieces of information are unknown. This paper fills the gap. In the proposed method, we model the unknown groups by latent classes and introduce item-specific DIF parameters to capture the DIF effects. Assuming the number of DIF items is relatively small, an $L_1$-regularised estimator is proposed to simultaneously identify the latent classes and the DIF items. A computationally efficient Expectation-Maximisation (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

翻译：测量工具（如调查问卷或教育测试）的有效性取决于项目层面的测量不变性。通常通过项目功能差异（DIF）分析来评估项目层面的测量不变性。传统DIF分析方法需要已知比较群体（参照群体和焦点群体）以及锚题（一组无DIF项目）。此类先验信息并非总可获得。当其中一项信息未知时，心理测量学方法已提出用于DIF分析。具体而言，当比较群体未知但锚题已知时，可采用潜在DIF分析方法，通过潜在类别估计未知群体；当锚题未知但比较群体已知时，通常在稀疏性假设（DIF项目数量较少）下提出相应方法。然而，当两项信息均未知时，尚无针对DIF分析的方法。本文填补了这一空白。在所提出的方法中，我们通过潜在类别对未知群体建模，并引入项目特定DIF参数来捕捉DIF效应。假设DIF项目数量相对较少，提出一种基于L1正则化的估计量，以同时识别潜在类别和DIF项目。针对该正则化估计量中的非平滑优化问题，开发了计算高效的期望最大化（EM）算法。通过模拟研究及实际教育测试项目反应数据的应用，评估了所提方法的性能。