Abstract

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.

Highlights

  • Multilevel structural equation modeling (MSEM) has gained increasing attention over the last decades, as it combines advantages of multilevel modeling (MLM) and structural equation modeling (SEM)

  • In the following, we will only report a representative selection of the different analyses because the results not reported here lead to similar conclusions

  • In this study we investigated the overall model fit of MLR compared to maximum likelihood (ML) for nonlinear MSEM with interaction effects at a single level or at both levels simultaneously

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Summary

Introduction

Multilevel structural equation modeling (MSEM) has gained increasing attention over the last decades, as it combines advantages of multilevel modeling (MLM) and structural equation modeling (SEM) (cf. Muthén, 1994; Mehta and Neale, 2005; Hox et al, 2010). For the analysis of nonlinear single-level SEM with interaction or quadratic effects in the structural model, several methods have been developed (for an overview see, e.g., Schumacker and Marcoulides, 1998; Marsh et al, 2004; Klein and Muthén, 2007; Moosbrugger et al, 2009; Brandt et al, in press). For the analysis of nonlinear MSEM only these two approaches have already been applied

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