A general non-linear multilevel structural equation mixture model - Kelava, Augustin; Brandt, Holger (Frontiers in Psychology, 2014)
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 nonlinear interaction and quadratic effects (e.g., Klein & Moosbrugger, 2000), and multilevel modeling (Rabe-Hesketh, Skrondal, & Pickles, 2004). We present a general nonlinear multilevel structural equation mixture model (GNM-SEMM) that combines recent semiparametric nonlinear structural equation models (Kelava & Nagengast, 2012; Kelava, Nagengast, & Brandt, in press) with multilevel structural equation mixture models (B. O. Muthén & 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.