Mixture multigroup structural equation modeling: A novel method for comparing structural relations across many groups

Area of Science:

• Behavioral Science
• Psychometrics
• Quantitative Psychology

Background:

• Structural equation modeling (SEM) is standard for examining latent variable relations.
• Comparing structural relations across many groups is common, but differences and similarities (clusters) exist.
• Measurement invariance is crucial for valid cross-group comparisons, yet often violated.

Purpose of the Study:

• To introduce Mixture Multigroup Structural Equation Modeling (MMG-SEM) for clustering groups based on structural relations.
• To address the challenge of measurement noninvariance when comparing structural relations across multiple groups.
• To provide a method that ensures valid clustering unaffected by measurement differences.

Main Methods:

• Proposes an estimation procedure for MMG-SEM using the R package "lavaan".
• Employs cluster-specific structural relations and group-specific measurement parameters.
• Evaluates performance through two simulation studies.

Main Results:

• MMG-SEM successfully recovers group clusters based on structural relations.
• The method accurately identifies cluster-specific structural relations.
• Partially group-specific measurement parameters are effectively captured.

Conclusions:

• MMG-SEM provides a valid approach to clustering groups by structural relations, accounting for measurement noninvariance.
• The method enhances the accuracy of cross-group comparisons in behavioral science.
• Empirical application demonstrates MMG-SEM's utility in cross-cultural research.