Zhao Hongwei, Vermunt Jeroen K, De Roover Kim
Quantitative Psychology and Individual Differences, KU Leuven, Leuven, Belgium.
Department of Methodology and Statistics, Tilburg University, Tilburg, Netherlands.
Front Psychol. 2025 Jul 28;16:1463790. doi: 10.3389/fpsyg.2025.1463790. eCollection 2025.
Structural equation modeling (SEM) is commonly used to explore relations between latent variables, such as beliefs and attitudes. However, comparing structural relations across a large number of groups, such as countries or classrooms, can be challenging. Existing SEM approaches may fall short, especially when measurement non-invariance is present. In this paper, we propose Mixture Multilevel SEM (MixML-SEM), a novel approach to comparing relationships between latent variables across many groups. MixML-SEM gathers groups with the same structural relations in a cluster, while accounting for measurement non-invariance in a parsimonious way by means of random effects. Specifically, MixML-SEM captures measurement non-invariance using multilevel confirmatory factor analysis and, then, it estimates the structural relations and mixture clustering of the groups by means of the structural-after-measurement approach. In this way, MixML-SEM ensures that the clustering is focused on structural relations and unaffected by differences in measurement. In contrast, Multilevel SEM (ML-SEM) estimates measurement and structural models simultaneously, and both with random effects. In comparison to ML-SEM, MixML-SEM provides better estimates of the structural relations, especially when (some of) the groups are large. This is because combining information from multiple groups within a cluster leads to more accurate estimates of the structural relations, whereas, in case of ML-SEM, these estimates are affected by shrinkage bias. We demonstrate the advantages of MixML-SEM through simulations and an empirical example on how social pressure to be happy relates to life satisfaction across 40 countries.
结构方程模型（SEM）通常用于探索潜在变量之间的关系，如信念和态度。然而，比较大量群体（如国家或教室）之间的结构关系可能具有挑战性。现有的SEM方法可能存在不足，尤其是在存在测量非不变性的情况下。在本文中，我们提出了混合多水平结构方程模型（MixML-SEM），这是一种用于比较多个群体中潜在变量之间关系的新方法。MixML-SEM将具有相同结构关系的群体聚集在一个聚类中，同时通过随机效应以简约的方式考虑测量非不变性。具体而言，MixML-SEM使用多水平验证性因子分析来捕捉测量非不变性，然后通过测量后结构方法估计群体的结构关系和混合聚类。通过这种方式，MixML-SEM确保聚类专注于结构关系，不受测量差异的影响。相比之下，多水平结构方程模型（ML-SEM）同时估计测量模型和结构模型，并且两者都采用随机效应。与ML-SEM相比，MixML-SEM对结构关系提供了更好的估计，尤其是当（某些）群体规模较大时。这是因为在一个聚类中合并多个群体的信息会导致对结构关系的估计更准确，而在ML-SEM的情况下，这些估计会受到收缩偏差的影响。我们通过模拟和一个关于40个国家中追求幸福的社会压力与生活满意度之间关系的实证例子，展示了MixML-SEM的优势。
