Estimation of nonlinear effects in latent variable models when data are non-normally distributed

• Applicant: Professor Dr. Augustin Kelava, since 8/2016
• Subject Area: Personality Psychology, Clinical and Medical Psychology, Methodology
• Term: from 2012 to 2018
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 230533471

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. This research project addresses the following extensions of (nonlinear) latent variable models: A general nonlinear multilevel structural equation mixture model 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.

• DFG Programme: Research Grants
• Ehemaliger Antragsteller: Professor Dr. Holger Brandt, until 7/2016