Comparing Factor Score Approaches to SEM in Multigroup Models with Small Samples

Factor Score Regression (FSR) is increasingly employed as an alternative to structural equation modeling (SEM) in small samples. Despite its popularity in psychology, the performance of FSR in multigroup models with small samples remains relatively unknown. The goal of this study was to examine the performance of FSR, namely Croon's correction and the bias avoiding method, for multigroup models with small samples and compare the methods to SEM. We conducted two simulation studies to evaluate how the sample size, proportion of invariant items, reliability, number of indicators, and measurement model misspecifications affect conclusions about the structural relationships in multigroup models. Additionally, we extended the methods to a multigroup actor-partner interdependence model. Results suggest that Croon's correction generally outperforms conventional SEM and the bias avoiding method in terms of bias, efficiency, Type I error, and coverage, especially in more complex multigroup models and under difficult estimation conditions.