Title: nlsem: An R Package for Nonlinear Structural Equation Mixture Models

Author: Katharina Naumann, Nora Umbach, David Hoppe, Holger Brandt, Augustin Kelava, Bernhard Schmitz

Affiliation: University of Tuebingen

Abstract: We introduce an R package for estimating nonlinear Structural
Equation Mixture Models via an Expectation-Maximization algorithm
(Dempster, Laird, & Rubin, 1977).  Implemented are three different model
approaches: Firstly, the Latent Moderated Structural Equations approach
(LMS; Klein & Moosbrugger, 2000), which allows for two-way interaction and
quadratic effects in structural models with normally distributed predictor
variables.

Secondly, the Structural Equation finite Mixture Model (STEMM or SEMM)
approach (Bauer, 2005; Jedidi, Jagpal, & DeSarbo, 1997), which uses
mixtures of linear structural equation models.  In this way it can deal
either with heterogeneity of linear relationships or approximate
simultaneously the nonnormality of the latent variables and their nonlinear
relationship.

And thirdly, the recently proposed Nonlinear Structural Equation Mixture
Model approach (NSEMM; Kelava, Nagengast, & Brandt, 2014).  Here,
interaction and quadratic terms as well as latent mixtures can be modeled,
which allows for a separation of nonnormality of the latent predictors and
nonlinearity of latent relationships.

In this talk, the user interface of the nlsem package and its main
functions will be presented, as well as data from a simulation study.
Limitations and future features of the proposed nlsem package will be
discussed.

References:
Bauer, D. J. (2005). A semiparametric approach to modeling nonlinear relations
    among latent variables. Structural Equation Modeling, 12, 513-535.
Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977). Maximum likelihood from
    incomplete data via the EM algorithm. Journal of the Royal Statistical
    Society, Series B, 39, 1-38.
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 nonnormally distributed latent
    predictor variables. Structural Equation Modeling: A Multidisciplinary
    Journal, 21, 468-481.
Klein, A., & Moosbrugger, H. (2000). Maximum likelihood estimation of latent
    interaction effects with the LMS method. Psychometrika, 65, 457-474.