Model Fit Estimation for Multilevel Structural Equation Models.

Area of Science:

• Psychometrics
• Multilevel Modeling
• Structural Equation Modeling (SEM)

Background:

• Structural Equation Modeling (SEM) is a powerful statistical technique for analyzing complex relationships between observed and latent variables.
• Multilevel SEM extends SEM to handle nested data structures, accounting for variations across multiple levels of analysis.
• Assessing model fit in multilevel SEM is challenging, as traditional indices often fail to adequately evaluate fit at each distinct level.

Purpose of the Study:

• To review and implement a partially-saturated model fit approach for multilevel SEM.
• To address the limitations of traditional model fit indices in multilevel contexts.
• To provide a computational method for assessing model fit at each level of analysis in 2-level SEM.

Main Methods:

• Review of the partially-saturated model fit approach (Ryu & West, 2009).
• Description of an alternative model parameterization that simplifies the multilevel data structure.
• Implementation of an algorithm for computing partially-saturated model fit in the OpenMx package for 2-level SEM.
• Verification through a simulation study and an empirical application using ecological momentary assessment data.

Main Results:

• The developed algorithm successfully computes partially-saturated model fit for 2-level SEM.
• The simulation study validated the implementation and its accuracy.
• The empirical application demonstrated the utility of the approach in evaluating affect structure theories.

Conclusions:

• The partially-saturated model fit approach offers a viable solution for assessing model fit in multilevel SEM.
• This method enhances the interpretability and accuracy of multilevel SEM analyses.
• The implemented algorithm in OpenMx provides a practical tool for researchers working with complex, nested data.