Evaluation of model fit in nonlinear multilevel structural equation modeling

  • Evaluating model fit in nonlinear multilevel structural equation models (MSEM) presents a challenge as no adequate test statistic is available. Nevertheless, using a product indicator approach a likelihood ratio test for linear models is provided which may also be useful for nonlinear MSEM. The main problem with nonlinear models is that product variables are non-normally distributed. Although robust test statistics have been developed for linear SEM to ensure valid results under the condition of non-normality, they have not yet been investigated for nonlinear MSEM. In a Monte Carlo study, the performance of the robust likelihood ratio test was investigated for models with single-level latent interaction effects using the unconstrained product indicator approach. As overall model fit evaluation has a potential limitation in detecting the lack of fit at a single level even for linear models, level-specific model fit evaluation was also investigated using partially saturated models. Four population models were considered: a model with interaction effects at both levels, an interaction effect at the within-group level, an interaction effect at the between-group level, and a model with no interaction effects at both levels. For these models the number of groups, predictor correlation, and model misspecification was varied. The results indicate that the robust test statistic performed sufficiently well. Advantages of level-specific model fit evaluation for the detection of model misfit are demonstrated.

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Author:Karin Schermelleh-Engel, Martin Kerwer, Andreas G. Klein
Pubmed Id:https://pubmed.ncbi.nlm.nih.gov/24624110
Parent Title (English):Frontiers in psychology
Publisher:Frontiers Research Foundation
Place of publication:Lausanne
Document Type:Article
Year of Completion:2014
Date of first Publication:2014/03/04
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2019/10/24
Tag:interaction effect; level-specific model fit; likelihood ratio test; multilevel structural equation modeling; robust test statistic
Issue:Article 181
Page Number:11
Dewey Decimal Classification:1 Philosophie und Psychologie / 15 Psychologie / 150 Psychologie
Licence (German):License LogoCreative Commons - Namensnennung 4.0