Finite Normal Mixture SEM Analysis by Fitting Multiple Conventional SEM Models.

Area of Science:

• Statistics
• Quantitative Psychology
• Econometrics

Background:

• Structural Equation Modeling (SEM) traditionally assumes data normality.
• Normal mixture SEM extends SEM to handle non-normal data but is sensitive to model misspecification.
• Existing methods struggle with distributional violations and model complexity.

Purpose of the Study:

• To propose a novel two-stage maximum likelihood (ML) approach for normal mixture SEM.
• To develop statistical inference robust to distributional misspecification.
• To enhance model evaluation and flexibility in mixture modeling.

Main Methods:

• A two-stage ML estimation process is introduced.
• Stage-1 estimates saturated means and covariances with a sandwich-type covariance matrix.
• Stage-2 evaluates structural models using stage-1 outputs, allowing conventional SEM diagnostics.

Main Results:

• The two-stage ML approach yields accurate models despite violated normal mixture assumptions and initial misspecification.
• It demonstrates computational efficiency and avoids confounding model specification with component number.
• The Bayesian Information Criterion (BIC) shows improved robustness to distribution violations at moderate sample sizes.

Conclusions:

• The proposed two-stage ML method offers a flexible and robust alternative for normal mixture SEM.
• It effectively handles distributional misspecification and model complexity.
• This framework facilitates the integration of new developments in mixture modeling literature.