Fitting structural equation mixture models

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Description

Estimation of structural equation models with nonlinear effects and underlying nonnormal distributions.

Details

This is a package for estimating nonlinear structural equation mixture models using an expectation-maximization (EM) algorithm. Four different approaches are implemented. Firstly, the Latent Moderated Structural Equations (LMS) approach (Klein & Moosbrugger, 2000) and the Quasi-Maximum Likelihood (QML) approach (Klein & Muthen, 2007), which allow for two-way interaction and quadratic terms in the structural model. Due to the nonlinearity, the latent criterion variables cannot be assumed to be normally distributed. Therefore, the latent criterins's distribution is approximated with a mixture of normal distributions in LMS. Secondly, the Structural Equation finite Mixture Model (STEMM or SEMM) approach (Jedidi, Jagpal & DeSarbo, 1997), which uses mixtures to model latent classes. In this way it can deal with heterogeneity in the sample or nonlinearity and nonnormality of the latent variables and their indicators. And thirdly, a combination of these two approaches, the Nonlinear Structural Equation Mixture Model (NSEMM) approach (Kelava, Nagengast & Brandt, 2014). Here, interaction and quadratic terms as well as latent classes can be modeled.

The models can be specified with specify_sem. Depending on the specification of interaction and the number of latent classes (num.classes) the returned object will be of class singleClass, semm, or nsemm. Each of these can be estimated using em and models of type singleClass can additionally be fitted with the function qml.

Future Features

  • NSEMM, LMS and QML for more than one latent endogenous variable.

  • Parameter standardization.

References

Jedidi, K., Jagpal, H. S., & DeSarbo, W. S. (1997). STEMM: A General Finite Mixture Structural Equation Model, Journal of Classification, 14, 23–50.

Kelava, A., Nagengast, B., & Brandt, H. (2014). A nonlinear structural equation mixture modeling approach for non-normally distributed latent predictor variables. Structural Equation Modeling, 21, 468-481.

Klein, A. &, Moosbrugger, H. (2000). Maximum likelihood estimation of latent interaction effects with the LMS method. Psychometrika, 65, 457–474.

Klein, A. &, Muthen, B. O. (2007). Quasi-Maximum Likelihood Estimation of Structural Equation Models With Multiple Interaction and Quadratic Effects Multivariate Behavioral Research, 42, 647–673.