Aligned-Exploratory Structural Equation Modeling: Integration of Multiple-group ESEM and Alignment

When certain noninvariant parameters exist in multiple-group ESEM model, strong measurement invariance model struggles to yield precise estimates of intercepts and factor means. Conversely, traditional alignment method cannot accurately estimate factor loadings, factor covariances, or factor mean parameters when the model contains cross loadings. This article systematically elaborates on the theoretical principles and computational procedures of multi-group CFA, multi-group ESEM, traditional alignment method, and aligned-ESEM. It summarizes the advantages of integrating the alignment method with multiple-group ESEM: bypassing the strong measurement invariance assumption for measurement invariance testing and multi-group comparisons; utilizing well-fitting configural invariance model for analysis; providing more accurate estimates of primary loadings, cross-loadings, noninvariant parameters, factor covariances, and factor means; and offering diagnostic insights into parameter-specific invariance/non-invariance within the model. Finally, using a study on work values among Chinese undergraduates as an example, the implementation steps of aligned-ESEM in Mplus are demonstrated, confirming the method’s applicability when strong measurement invariance conditions are unmet.