Regularized Structural Equation Models

Structural equation models are frequently used in psychology for cross-sectional and longitudinal data analysis because they can take into account measurement error and represent a range of assumed relationships between psychological constructs. However, when using structural equation models, many modeling decisions are required from the user and for which sufficient information is not always available. To mitigate this problem, structural equation models can be combined with regularizing estimation procedures, which in addition to optimizing model fit to the data can simultaneously produce models that are as parsimonious as possible. This combines the steps of estimation and model selection. Regularized structural equation models therefore allow a "semi-confirmatory" approach, where one can make modeling decisions for which little information is available in a data-driven manner. This is potentially useful for psychological research because existing knowledge can be optimally exploited without necessarily making all modeling decisions a priori.

In the project, the usefulness of regularized structural equation models for typical psychological applications will be (further) investigated (e.g., in the context of questionnaire development). Among other things, simulation studies will be conducted to investigate the performance in comparison to other established or proposed methods.

Relevant publications:

Scharf, F., & Nestler, S. (2019c). Should regularization replace simple structure rotation in exploratory factor analysis? Structural Equation Modeling: A Multidisciplinary Journal, 26, 576-590.

Scharf, F.*, Pförtner, J.*, & Nestler, S. (2021). Can ridge and elastic net structural equation modeling be used to stabilize parameter estimates when latent factors are correlated? Structural Equation Modeling: A Multidisciplinary Journal, 62, 928-940. (*shared first authorship).