Conventional approaches for selecting a reference indicator (RI) could lead to misleading results in testing for measurement invariance (MI). Several newer quantitative methods have been available for more rigorous RI selection. However, it is still unknown how well these methods perform in terms of correctly identifying a truly invariant item to be an RI. Thus, Study 1 was designed to address this issue in various conditions using simulated data. As a follow-up, Study 2 further investigated the advantages/disadvantages of using RI-based approaches for MI testing in comparison with non-RI-based approaches. Altogether, the two studies provided a solid examination on how RI matters in MI tests. In addition, a large sample of real-world data was used to empirically compare the uses of the RI selection methods as well as the RI-based and non-RI-based approaches for MI testing. In the end, we offered a discussion on all these methods, followed by suggestions and recommendations for applied researchers.

中文翻译：

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重要：测量不变性测试中的参考指标选择

选择参考指标 (RI) 的传统方法可能会导致在测试测量不变性 (MI) 时产生误导性结果。几种较新的定量方法可用于更严格的 RI 选择。然而，这些方法在正确识别真正不变的项目为 RI 方面的表现如何仍然未知。因此，研究 1 旨在使用模拟数据在各种条件下解决这个问题。作为后续研究，研究 2 进一步调查了使用基于 RI 的方法进行 MI 测试与非基于 RI 的方法相比的优势/劣势。总之，这两项研究对 RI 在 MI 测试中的重要性提供了可靠的检验。此外，大量真实数据样本用于经验比较 RI 选择方法以及基于 RI 和非基于 RI 的 MI 测试方法的使用。最后，我们对所有这些方法进行了讨论，然后对应用研究人员提出了建议和建议。