Abstract
Structural equation mixture modeling (SEMM) has become a standard procedure in latent variable modeling over the last two decades (Jedidi, Jagpal, and DeSarbo 1997b; Muthén and Shedden 1999; Muthén 2001, 2004; Muthén and Asparouhov 2009). SEMM was proposed as a technique for the approximation of nonlinear latent variable relationships by finite mixtures of linear relationships (Bauer 2005, 2007; Bauer, Baldasaro, and Gottfredson 2012). In addition to this semiparametric approach to nonlinear latent variable modeling, there are numerous parametric nonlinear approaches for normally distributed variables (e.g., LMS in Mplus; Klein and Moosbrugger 2000). Recently, an additional semiparametric nonlinear structural equation mixture modeling (NSEMM) approach was proposed by Kelava, Nagengast, and Brandt (2014) that is capable of dealing with nonnormal predictors. In the nlsem package presented here, the SEMM, two distribution analytic (QML and LMS) and NSEMM approaches can be specified and estimated. We provide examples of how to use the package in the context of nonlinear latent variable modeling.
Highlights
The analysis of nonlinear relationships between latent variables in the structural equation modeling (SEM) framework has been conducted primarily with two different classes of models
An integration of parametric and semiparametric approaches that allows for the explicit formulation of nonlinear relations and simultaneously accounts for nonnormality of the data with semiparametric mixture models is called nonlinear structural equation mixture modeling (NSEMM)
We fitted a model with two latent classes, one interaction effect, and two quadratic effects to the data applying the NSEMM approach
Summary
The analysis of nonlinear relationships between latent variables in the structural equation modeling (SEM) framework has been conducted primarily with two different classes of models. For the purpose of assessing these parametric nonlinear effects, a variety of approaches have been developed such as the product-indicator approaches (e.g., Bollen 1995; Jaccard and Wan 1995; Jöreskog and Yang 1996; Kelava and Brandt 2009; Kenny and Judd 1984; Little, Bovaird, and Widaman 2006; Marsh et al 2004, 2006; Ping 1995, 1996; Wall and Amemiya 2001), distribution-analytic approaches (Klein and Moosbrugger 2000; Klein and Muthén 2007), moment-based approaches (Mooijaart and Bentler 2010; Wall and Amemiya 2000, 2003), and Bayesian approaches (Arminger and Muthén 1998; Lee 2007) For these kinds of models, the functional relationship (e.g., quadratic) needs to be specified a priori, and the size of the nonlinear effects can be calculated (Wen, Marsh, and Hau 2010). Parametric and semiparametric approaches to dealing with nonlinearity in a SEM framework will be introduced in more detail
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