Behavioral scientists often examine the relations between two or more latent variables (e.g., how emotions relate to life satisfaction), and structural equation modeling (SEM) is the state-of-the-art for doing so. When comparing these "structural relations" among many groups, they likely differ across the groups. However, it is equally likely that some groups share the same relations so that clusters of groups emerge. Latent variables are measured indirectly by questionnaires and, for validly comparing their relations among groups, the measurement of the latent variables should be invariant across the groups (i.e., measurement invariance). However, across many groups, often at least some measurement parameters differ. Restricting these measurement parameters to be invariant, when they are not, causes the structural relations to be estimated incorrectly and invalidates their comparison. We propose mixture multigroup SEM (MMG-SEM) to gather groups with equivalent structural relations in clusters while accounting for the reality of measurement noninvariance. Specifically, MMG-SEM obtains a clustering of groups focused on the structural relations by making them cluster-specific, while capturing measurement noninvariances with group-specific measurement parameters. In this way, MMG-SEM ensures that the clustering is valid and unaffected by differences in measurement. This article proposes an estimation procedure built around the R package "lavaan" and evaluates MMG-SEM's performance through two simulation studies. The results demonstrate that MMG-SEM successfully recovers the group-clustering as well as the cluster-specific relations and the partially group-specific measurement parameters. To illustrate its empirical value, we apply MMG-SEM to cross-cultural data on the relations between experienced emotions and life satisfaction. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

中文翻译：

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混合多组结构方程建模：一种比较多组结构关系的新方法。


行为科学家经常检查两个或多个潜在变量之间的关系（例如，情绪与生活满意度的关系），而结构方程模型（SEM）是最先进的方法。当比较许多群体之间的这些“结构关系”时，它们可能在不同群体之间有所不同。然而，同样可能的是，一些群体具有相同的关系，从而出现群体集群。潜变量是通过问卷间接测量的，为了有效比较组间的关系，潜变量的测量应该在组间保持不变（即测量不变性）。然而，在许多群体中，通常至少有一些测量参数是不同的。限制这些测量参数不变，如果它们不不变，则会导致结构关系估计不正确并使它们的比较无效。我们提出混合多组 SEM（MMG-SEM）来收集簇中具有等效结构关系的组，同时考虑测量非不变性的现实。具体来说，MMG-SEM 通过使它们具有特定于簇的结构关系来获得专注于结构关系的组的聚类，同时使用特定于组的测量参数捕获测量非不变性。通过这种方式，MMG-SEM确保聚类有效并且不受测量差异的影响。本文提出了一种围绕 R 包“lavaan”构建的估计程序，并通过两项模拟研究评估 MMG-SEM 的性能。结果表明，MMG-SEM 成功地恢复了组聚类以及特定于簇的关系和部分特定于组的测量参数。 为了说明其经验价值，我们将 MMG-SEM 应用于有关体验情绪与生活满意度之间关系的跨文化数据。 （PsycInfo 数据库记录 (c) 2024 APA，保留所有权利）。