Mixture multigroup structural equation modeling: A novel method for comparing structural relations across many groups.

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).

Beyond Pearson's Correlation: Modern Nonparametric Independence Tests for Psychological Research.

When examining whether two continuous variables are associated, tests based on Pearson's, Kendall's, and Spearman's correlation coefficients are typically used. This paper explores modern nonparametric independence tests as an alternative, which, unlike traditional tests, have the ability to potentially detect any type of relationship. In addition to existing modern nonparametric independence tests, we developed and considered two novel variants of existing tests, most notably the Heller-Heller-Gorfine-Pearson (HHG-Pearson) test. We conducted a simulation study to compare traditional independence tests, such as Pearson's correlation, and the modern nonparametric independence tests in situations commonly encountered in psychological research. As expected, no test had the highest power across all relationships. However, the distance correlation and the HHG-Pearson tests were found to have substantially greater power than all traditional tests for many relationships and only slightly less power in the worst case. A similar pattern was found in favor of the HHG-Pearson test compared to the distance correlation test. However, given that distance correlation performed better for linear relationships and is more widely accepted, we suggest considering its use in place or additional to traditional methods when there is no prior knowledge of the relationship type, as is often the case in psychological research.