Title: A general non-linear multilevel structural equation mixture model
Authors: Augustin Kelava - Eberhard Karls Universitaet Tuebingen (Germany) [presenting]
Holger Brandt - Eberhard Karls Universitaet Tuebingen (Germany)
Abstract: In the past two 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 either a) nonlinear interaction and quadratic effects, b) multilevel effects, or c) mixtures. In recent years, (linear) parametric multilevel structural equation mixture model frameworks have been presented and made available in popular statistical latent variable modeling software. Nevertheless, these frameworks are restricted to parametric linear relationships. A general nonlinear multilevel structural equation mixture model (GNM-SEMM) is presented that combines recent semiparametric nonlinear structural equation models with multilevel structural equation mixture models for clustered and nonnormally distributed data. The proposed approach allows for semiparametric nonlinear relationships at the within and at the between levels. Examples from the educational science are presented to illustrate different submodels from the general framework.