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.

A Marginal Maximum Likelihood Approach for Extended Quadratic Structural Equation Modeling with Ordinal Data

“…Studies mentioned above are devoted to single group data analysis. It is further generalized by Song and Lee (2006b) to multigroup analysis and by Kelava and Brandt (2014), Lee and Song (2004b), Lee et al (2009), and Song and Lee (2004) to multilevel analysis.…”

Simulation Study to Describe Bayesian Analysis of Nonlinear Structural Equation Modeling

“…Due to the complex distributions associated with the nonlinear latent variables, methods for analyzing such this structural equation modeling are become more difficult [5]. Several methods for the analysis of nonlinear SEM have been published, such as distribution analytic approaches [6], the product indicator approaches [7], moment based approaches [8] and Bayesian approaches [9]. More recently, methods that used the LISREL program have been proposed to analyzed some nonlinear structural equation models with interaction terms of latent variables.…”

The Standardization of Linear and Nonlinear Effects in Direct and Indirect Applications of Structural Equation Mixture Models for Normal and Nonnormal Data

“… The application of mixture models to flexibly estimate linear and nonlinear effects in the SEM framework has received increasing attention (e.g., Jedidi et al, 1997b ; Bauer, 2005 ; Muthén and Asparouhov, 2009 ; Wall et al, 2012 ; Kelava and Brandt, 2014 ; Muthén and Asparouhov, 2014 ). The advantage of mixture models is that unobserved subgroups with class-specific relationships can be extracted (direct application), or that the mixtures can be used as a statistical tool to approximate nonnormal (latent) distributions (indirect application).…”

“…The estimation of nonlinear latent effects in the structural equation modeling (SEM) framework has received increasing attention over the last three decades. Several approaches for the analysis of nonlinear SEM have been published, which include among others the product indicator approaches (e.g., Kenny and Judd, 1984 ; Bollen, 1995 ; Jaccard and Wan, 1995 ; Jöreskog and Yang, 1996 ; Ping, 1995 , 1996 ; Wall and Amemiya, 2001 ; Marsh et al, 2004 ; Little et al, 2006 ; Marsh et al, 2006 ; Kelava and Brandt, 2009 ), distribution analytic approaches (Klein and Moosbrugger, 2000 ; Klein and Muthén, 2007 ), moment based approaches (Wall and Amemiya, 2000 , 2003 ; Mooijaart and Bentler, 2010 ), and Bayesian approaches (Arminger and Muthén, 1998 ; Lee, 2007 ; Kelava and Nagengast, 2012 ; Kelava and Brandt, 2014 ).…”