In the past years, there was a growing insight that using linear latent variable models did not suffice neither to answer detailed research questions nor to account for the challenges of complex empirical data. Typical challenges are multilevel data structures, non-normal data and nonlinear relationships between variables. The modeling of such data specifities has two advantages: First, if these data specificites were neglected, the results and conclusion drawn by the researchers might be spurious. And, second, a more detailed modeling allows for a more in-depth analysis of research questions, for example, by identifying unobserved subgroups or the differentiation of nonlinear relationships on individual and cluster level.

The NON-NORM research project addresses the following extensions of (nonlinear) latent variable models: A general nonlinear multilevel structural equation mixture model (GNM-SEMM) will be extended to allow for an analysis of longitudinal heteroskedastic data. An R-package will be provided for substantial researchers. Semiparametric structural equation models will be generalized to non-Bayesian, nonparametric, distribution-free structural equation models. The finite sample properties of the developed semi- and nonparametric models will be examined in simulation studies. Finally, multidimensional item response models will be extended to allow for nonlinear semiparametric effects.

Funded by The Deutsche Forschungsgemeinschaft (DFG): BR 5175-1-2, KE 1664/1-1, KE 1664/1-2

Status: April 1, 2013 – July 31, 2018 (completed)

Project team

Holger Brandt, Augustin Kelava, Stefano Noventa, Tim Schaffland, & Nora Umbach


nlsem: Fitting Structural Equation Mixture Models – Estimation of structural equation models with nonlinear effects and underlying nonnormal distributions.


Matlab: An implementation of the non-parametric structural equation modeling approach (Kelava, Kohler, Krzyzak, & Schaffland, 2017) can be found here:

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