Comparison of frequentist and Bayesian regularization in structural equation modeling.

Area of Science:

• Statistical modeling
• Psychometrics
• Computational statistics

Background:

• Regularization techniques are increasingly vital in structural equation modeling (SEM).
• Limited research compares regularization across frequentist and Bayesian estimation frameworks.
• Recent advancements in Bayesian regularization warrant focused investigation.

Purpose of the Study:

• To compare regularization approaches (ridge, lasso) in SEM across frequentist and Bayesian estimation.
• To identify similarities and distinctions between these estimation frameworks.
• To highlight recent developments in Bayesian regularization methods.

Main Methods:

• Utilized two empirical examples to demonstrate regularization techniques.
• Applied both ridge and lasso regularization methods.
• Compared frequentist and Bayesian estimation approaches for SEM.

Main Results:

• Demonstrated practical application of ridge and lasso regularization in SEM.
• Illustrated similarities and differences in parameter estimates and model fit across estimation frameworks.
• Provided insights into software implementation for Bayesian regularization.

Conclusions:

• Regularization in SEM shows both convergence and divergence between frequentist and Bayesian methods.
• Further research is needed to synthesize findings across both frameworks.
• Advocates for increased cross-framework evaluation to advance SEM methodology.