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

AbstractFactor 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.Keywords: Croon's correctionfactor score regressionmultigroup modelssmall samplesstructural equation modeling Disclosure statementNo potential conflict of interest was reported by the authors.Notes1 https://osf.io/fcujz/.2 When a different identification strategy was used in Study 1, factor reflection was detected less than 1% of the time. Factor reflection was identified by evaluating whether the average value of the loadings for the exogenous and endogenous variable items was of opposite signs. In these cases, the sign of the structural path estimate was flipped, and bias and coverage were recomputed. We provide supplemental files with the results from our factor reflection analysis. The pattern of results was consistent with those presented in the main text.