Abstract

Structural equation modeling (SEM) relies on accurate model specification and appropriate data to ensure stable parameter estimation. However, in practice, these ideal conditions are often difficult to satisfy, leading to frequent issues with estimation instability. In recent years, regularization techniques have emerged as a promising solution to enhance estimation stability in SEM, drawing increasing attention in the field. Despite their potential, regularization methods remain unfamiliar to many researchers, and applying them effectively to address estimation challenges is not yet commonplace. This study aims to bridge this gap by providing a comprehensive overview of regularization techniques and proposing practical approaches for their application in the context of frequentist SEM. Specifically, we distinguish between regularized maximum likelihood estimation and regularized least squares estimation, outlining how each can be utilized to mitigate instability. We also identify key sources of estimation instability in SEM and explore how regularization can be applied in response to specific instability scenarios, offering corresponding guidelines for implementation. Finally, an empirical example using real data is presented to illustrate the full analytical procedure of regularized SEM. Through a comparative analysis with conventional maximum likelihood estimation under a condition of instability, we demonstrate the practical advantages and effectiveness of regularization approaches.