Regularized Structural Equation Modeling

Abstract

We present a new method that extends the use of regularization in both lasso and ridge regression to structural equation modeling (SEM). This method, termed regularized structural equation modeling (RegSEM), penalizes specific parameters in structural equation models, with the goal of creating easier to understand and simpler models.

Key Innovation

RegSEM extends regularization to SEM by:

• Implementing both ridge and lasso penalties in structural equation models
• Enabling automatic parameter selection and model simplification
• Addressing overfitting in complex models with small samples
• Focusing on model generalizability rather than just model fit

Technical Contributions

• Parameter Penalties: Ridge and lasso regularization for any SEM parameter
• Model Selection: Automated approach to identifying important parameters
• Sparse Solutions: Lasso penalties can set parameters exactly to zero
• Generalizability Focus: Emphasis on cross-validation and out-of-sample prediction

Research Impact

• Most Cited Work: Foundation for extensive follow-up research
• R Package: The regsem package has become a standard tool in the field
• Methodological Advance: Addresses replication crisis through generalizability emphasis
• Field Influence: Sparked numerous applications and extensions

Practical Applications

RegSEM is particularly useful for:

• Large models with many parameters
• Small sample sizes relative to model complexity
• Exploratory model building
• Cross-validation and prediction contexts
• Addressing multicollinearity in SEM

Software Implementation

The method is implemented in the R package regsem, making it accessible to applied researchers. The package integrates with lavaan for easy implementation.

Recommended citation: Jacobucci, R., Grimm, K. J., & McArdle, J. J. (2016). “Regularized Structural Equation Modeling.” Structural Equation Modeling, 23(4), 555-566.