A Comparative Study of Bayesian Structural Equation Modeling, Aligned Exploratory Structural Equation Modeling, and Penalized Alignment Method

In 2023, the aligned exploratory structural equation modeling and penalized alignment method were proposed as new methods in the important field of measurement invariance testing in psychometrics and statistics. Researchers typically conduct measurement invariance testing on the fitted model of their data before making multiple-group comparisons of latent factor means in factor analysis. Although these new methods integrate the strengths of traditional approaches and overcome some of their limitations, their applicability and generalizability lack evidence from empirical research and Monte Carlo simulation studies. This article utilizes Monte Carlo simulation studies to investigate the performance of Bayesian structural equation modeling, aligned exploratory structural equation modeling, and penalized alignment method in different scenarios.First, data were generated in favor of Bayesian structural equation modeling, aligned exploratory structural equation modeling, and penalized alignment method respectively. Second, the preceding three models were used to fit the data in favor of the three models respectively. Comparisons of the three models were conducted.