A Comparison of Regularized Maximum-Likelihood, Regularized 2-Stage Least Squares, and Maximum-Likelihood Estimation...

Area of Science:

• Multivariate statistics
• Psychometrics
• Econometrics

Background:

• Structural equation modeling (SEM) methods are crucial for analyzing complex relationships.
• New estimation techniques like 2-stage least squares (2SLS) and regularization aim to improve SEM with model misspecification.
• Existing research often overlooks performance in small samples and with weak factor loadings, common in real-world data.

Purpose of the Study:

• To compare the performance of novel SEM estimation methods under conditions of small sample sizes and weak factor loadings.
• To evaluate regularized 2SLS and regularized SEM for misspecified models, including interactions and cross-loadings.
• To provide practical recommendations for applied researchers using these techniques.

Main Methods:

• A simulation study was conducted to compare estimation techniques.
• The study focused on misspecified structural equation models.
• Key conditions examined were small sample sizes and weak factor loadings.

Main Results:

• Regularized 2-stage least squares (2SLS) demonstrated superior performance compared to the regularized SEM framework.
• This advantage was particularly evident in scenarios with small samples and weak factor loadings.
• The findings highlight the effectiveness of regularized 2SLS in challenging data situations.

Conclusions:

• Regularized 2SLS is a recommended estimation method for structural equation modeling when dealing with small samples and weak factor loadings.
• Applied researchers should consider regularized 2SLS for improved model estimation accuracy in such common scenarios.
• The study provides valuable insights for selecting appropriate SEM techniques based on data characteristics.