Regularized structural equation modeling with stability selection

Regularization methods such as the least absolute shrinkage and selection operator (LASSO) are commonly used in high dimensional data to achieve sparser solutions. Recently, methods such as regularized structural equation modeling (SEM) and penalized likelihood SEM have been proposed, trying to transfer the benefits of regularization to models commonly used in social and behavioral research. These methods allow researchers to estimate large models even in the presence of small sample sizes. However, some drawbacks of the LASSO, such as high false positive rates (FPRs) and inconsistency in selection results, persist at the same time. We propose the application of stability selection, a method based on repeated resampling of the data to select stable coefficients, to regularized SEM as a mechanism to overcome these limitations. Across 2 simulation studies, we find that stability selection greatly improves upon the LASSO in selecting the correct paths, specifically through reducing the number of false positives. We close the article by demonstrating the application of stability selection in 2 empirical examples and presenting several future research directions. (PsycInfo Database Record (c) 2021 APA, all rights reserved).