People are variables too: multilevel structural equations modeling.

Area of Science:

• Statistics
• Psychometrics
• Quantitative Psychology

Background:

• Multilevel structural equation models (ML-SEM) are complex statistical tools.
• Confirmatory factor analysis (CFA) provides a structured framework for model analysis.
• General mixed-effects models share similarities with ML-SEM.

Purpose of the Study:

• To didactically explain ML-SEM using CFA as a template.
• To demonstrate the equivalence between general mixed-effects models and ML-SEM.
• To introduce a graphical representation for complex ML-SEMs.

Main Methods:

• Confirmatory factor analysis (CFA) as a didactic template.
• Extension of definition variables for ML-SEM with random slopes.
• Graphical representation of complex ML-SEMs.
• Empirical examples using SAS Proc Mixed, Mplus, and Mx.

Main Results:

• Demonstrated equivalence of general mixed-effects models and ML-SEM.
• Introduced an intuitive graphical representation for complex ML-SEMs.
• Extended definition variable usage to ML-SEMs with random slopes for clustered data.

Conclusions:

• ML-SEM can be effectively explained using a CFA template.
• Graphical representations enhance understanding of complex ML-SEMs.
• Methodological considerations for estimation and model fit in ML-SEM are crucial.