Methodological Advances with Penalized Structural Equation Models

Penalized structural equation models (PSEM) is a powerful technique that unlocks a variety of new modeling frameworks. PSEM applications have been established previously for standard SEM and ESEM models. In this note we aim to extend these ideas to more general types of models such as finite mixture models, multilevel models as well as models with more general types of outcomes. Maximum likelihood and weighted least squares estimation methods naturally accommodate a penalty term. In Mplus 8.12 the PSEM methodology is implemented for all models that can be estimated with these two estimators. Therefore we can now easily combine the more general models with the features of PSEM such as EFA, Alignment, and parameter invariance. Some additional basic SEM applications are also included.