Sparse estimation through regularization is gaining popularity in psychological research. Such techniques penalize the complexity of the model and could perform variable/path selection in an automatic way, and thus are particularly useful in models that have small parameter-to-sample-size ratios. This paper gives a detailed tutorial of the R package regsem, which implements regularization for structural equation models. Example R code is also provided to highlight the key arguments of implementing regularized structural equation models in this package. The tutorial ends by discussing remedies of some known drawbacks of a popular type of regularization, computational methods supported by the package that can improve the selection result, and some other practical issues such as dealing with missing data and categorical variables.

Regularization methods such as the least absolute shrinkage and selection operator (LASSO) are commonly used in high dimensional data to achieve sparser solutions. They are also becoming increasingly popular in social and behavioral research. 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 with latent variables involved. 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 use of stability selection (Meinshausen & B̈hlmann, 2010) as a mechanism to overcome these limitations, demonstrating simulation conditions in which it improves performance, and simulation conditions in which it does not. In this paper, we point out that there is no free lunch, and researchers should be aware of those problems when applying regularization to latent variable models, concluding with an empirical example and further discussion of the application of regularization to SEM.