Estimation of structural equation models with nonlinear effects and underlying nonnormal distributions.
NSEMM, LMS and QML for more than one latent endogenous variable.
Parameter standardization.
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.
Jedidi, K., Jagpal, H. S., & DeSarbo, W. S. (1997). STEMM: A General Finite Mixture Structural Equation Model, Journal of Classification, 14, 23--50. doi:http://dx.doi.org/10.1007/s003579900002
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. doi:http://dx.doi.org/10.1080/10705511.2014.915379
Klein, A. &, Moosbrugger, H. (2000). Maximum likelihood estimation of latent interaction effects with the LMS method. Psychometrika, 65, 457--474. doi:http://dx.doi.org/10.1007/bf02296338
Klein, A. &, Muthen, B. O. (2007). Quasi-Maximum Likelihood Estimation of Structural Equation Models With Multiple Interaction and Quadratic Effects. Multivariate Behavior Research, 42, 647--673. doi:http://dx.doi.org/10.1080/00273170701710205