title: A general non-linear multilevel structural equation mixture model.
abstract: In the past 2 decades latent variable modeling has become a standard tool in the social sciences. In the same time period, traditional linear structural equation models have been extended to include non-linear interaction and quadratic effects (e.g., Klein and Moosbrugger, 2000), and multilevel modeling (Rabe-Hesketh et al., 2004). We present a general non-linear multilevel structural equation mixture model (GNM-SEMM) that combines recent semiparametric non-linear structural equation models (Kelava and Nagengast, 2012; Kelava et al., 2014) with multilevel structural equation mixture models (Muthén and Asparouhov, 2009) for clustered and non-normally distributed data. The proposed approach allows for semiparametric relationships at the within and at the between levels. We present examples from the educational science to illustrate different submodels from the general framework.
authors.affiliation: Department of Education, Center for Educational Science and Psychology, Eberhard Karls Universität Tübingen Tübingen, Germany.
authors.forename: Augustin
authors.initials: A
authors.lastname: Kelava
authors.affiliation: Department of Education, Center for Educational Science and Psychology, Eberhard Karls Universität Tübingen Tübingen, Germany.
authors.forename: Holger
authors.initials: H
authors.lastname: Brandt
keywords: latent variables; mixture distribution; multilevel; non-linear; semiparametric; structural equation modeling
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