Evaluation of model fit in nonlinear multilevel structural equation modeling.

Area of Science:

• Multivariate Statistics
• Structural Equation Modeling

Background:

• Evaluating model fit in nonlinear multilevel structural equation models (MSEM) is difficult due to the lack of adequate test statistics.
• Nonlinear models present challenges with non-normally distributed product variables, complicating the application of existing robust test statistics developed for linear SEM.

Purpose of the Study:

• To investigate the performance of a robust likelihood ratio test for nonlinear MSEM using an unconstrained product indicator approach.
• To assess the utility of level-specific model fit evaluation in detecting model misfit within nonlinear MSEM.

Main Methods:

• A Monte Carlo simulation study was conducted to evaluate the robust likelihood ratio test.
• The study examined models with single-level latent interaction effects, varying factors like the number of groups, predictor correlation, and model misspecification.
• Partially saturated models were used to investigate level-specific model fit evaluation.

Main Results:

• The robust likelihood ratio test demonstrated sufficient performance in evaluating model fit for nonlinear MSEM.
• Level-specific model fit evaluation proved advantageous in detecting model misfit, even in the presence of overall model fit limitations.

Conclusions:

• The robust likelihood ratio test is a viable option for assessing model fit in nonlinear MSEM.
• Level-specific evaluation enhances the detection of model misspecification in multilevel models with interaction effects.