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    Area of Science:

    • Statistics
    • Quantitative Psychology
    • Econometrics

    Background:

    • Standard regression and structural equation models (SEM) assume independent residuals, which is often violated in practice.
    • Multilevel models (MLM) were developed to handle dependent data structures, but extending SEMs to such data presents challenges.
    • Longitudinal growth curve models in SEM and MLM are known to be analytically and empirically identical under many conditions.

    Purpose of the Study:

    • To investigate the source and implications of the analytical equivalence between SEM and MLM in the context of nested data.
    • To leverage this isomorphism to extend SEM capabilities to a broader range of nested data structures.
    • To explore the potential applications and future directions for multilevel SEMs.

    Main Methods:

    • Exploration of the analytical reasons for the equivalence between SEM and MLM in nested data, specifically repeated measures over time.
    • Utilizing the established isomorphism to develop extensions of SEM for general nested data.
    • Descriptive analysis of potential opportunities and future research avenues for multilevel SEM.

    Main Results:

    • The study elucidates why SEM and MLM growth curve models are analytically equivalent when dealing with nested data from repeated observations.
    • This understanding facilitates the extension of SEM to a wider array of nested data scenarios.
    • The findings pave the way for the development and application of multilevel SEMs.

    Conclusions:

    • The isomorphism between SEM and MLM in growth modeling provides a foundation for extending SEM to general nested data.
    • Multilevel SEM offers promising opportunities for analyzing complex data structures.
    • Further research is needed to fully realize the potential of multilevel SEMs.