Abstract

In longitudinal data analysis of multidimensional factor models, the simple structure assumed by independent clusters model of confirmatory factor analysis (ICM-CFA) often fails to adequately capture the complex factor structures present in real data. The constraint in ICM-CFA that each indicator variable loads on only one factor tends to yield poor model fit, particularly when combined with additional constraints such as longitudinal measurement invariance, and post hoc modifications to improve fit risk producing sample-specific results. This study introduces exploratory structural equation modeling (ESEM) and penalized structural equation modeling (PSEM) as approaches that systematically allow cross-loadings, and proposes their application to longitudinal data analysis of multidimensional factor structures. For illustrative purposes, the analysis used responses from 1,796 participants on items measuring positive and negative affect experience collected in 2008 and 2020 from the Health and Retirement Study (HRS) in the United States. The analyses demonstrated that ESEM and PSEM can provide superior model fit compared to ICM-CFA within a given model, and are particularly useful when imposing measurement invariance constraints. Furthermore, in the case of PSEM, by specifying a partial invariance model that imposes measurement invariance constraints only on primary loadings, it was shown that the core elements of the measurement structure can be held consistent while the invariance assumption for secondary relationships is relaxed. This study provides practical guidance for applying ESEM and PSEM in situations where relaxing the simple structure assumption is warranted in longitudinal multidimensional factor analysis. This approach reduces arbitrariness in the modification process of complex longitudinal factor models and enables systematic exploration of changes in multidimensional factor structures over time.