ABSTRACT

Comparisons of latent constructs across groups are ubiquitous in behavioral research and, nowadays, often numerous groups are involved. Measurement invariance of the constructs across the groups is imperative for valid comparisons and can be tested by multigroup factor analysis. Metric invariance (invariant factor loadings) often holds, whereas scalar invariance (invariant intercepts) is rarely supported across many groups. Scalar invariance is a prerequisite for comparing latent means, however. One may inspect group-specific intercepts to pinpoint non-invariances, but this is a daunting task in case of many groups. This paper presents mixture multigroup factor analysis (MMG-FA) for clustering groups based on their intercepts. Clusters of groups with scalar invariance are obtained by imposing cluster-specific intercepts and invariant loadings whereas unique variances, factor means, and factor (co)variances can differ between groups. Thus, MMG-FA ties down the number of intercepts to inspect and generates clusters of groups wherein latent means can be validly compared.

摘要

跨群体的潜在结构的比较在行为研究中无处不在，如今，通常涉及许多群体。跨组结构的测量不变性对于有效比较是必不可少的，并且可以通过多组因素分析进行​​测试。度量不变性（不变因子载荷）通常成立，而在许多组中很少支持标量不变性（不变截距）。然而，标量不变性是比较潜在均值的先决条件。人们可能会检查特定于组的拦截以查明非不变性，但在许多组的情况下，这是一项艰巨的任务。本文介绍了基于截距聚类组的混合多组因子分析 (MMG-FA)。具有标量不变性的组群是通过施加特定于集群的截距和不变载荷来获得的，而独特的方差、因子均值和因子（协）方差在组之间可能不同。因此，MMG-FA 限制了要检查的拦截次数并生成组群，其中可以有效地比较潜在均值。