Model fit evaluation in multilevel structural equation models.

Area of Science:

• Multivariate statistics
• Psychometrics
• Quantitative psychology

Background:

• Assessing model fit is crucial in structural equation modeling (SEM).
• The standard approach for multilevel SEM evaluates overall model fit, but struggles with higher levels due to smaller sample sizes.
• This can obscure where model misspecification occurs.

Purpose of the Study:

• To review and compare alternative approaches for assessing model fit in multilevel structural equation models.
• To address the limitations of the standard simultaneous fit assessment method.
• To provide guidance on selecting appropriate fit assessment strategies for multilevel SEM.

Main Methods:

• Review of two alternative approaches: a two-step procedure (Yuan & Bentler, 2007) and a level-specific approach using partially saturated models (Ryu & West, 2009).
• Analysis of simulation studies comparing the standard approach with the two alternative methods.
• Demonstration using an empirical example.

Main Results:

• The standard approach often fails to detect lack of fit at higher levels in multilevel SEM.
• Both the two-step procedure and the level-specific approach effectively identify misspecification at all model levels.
• Simulation studies consistently support the superiority of alternative methods for higher-level fit detection.

Conclusions:

• Alternative approaches (two-step and level-specific) are recommended for assessing model fit in multilevel SEM.
• These methods overcome the limitations of the standard simultaneous approach, particularly for higher-level models.
• Researchers should adopt these advanced techniques for more accurate model evaluation.