Exploratory structural equation modeling and the curse of dimensionality.

The next-generation approach to research in the behavioral sciences is based on intensive collections of data and complex models characterized by many parameters for a limited sample size. This introduces new challenges for traditional latent-variable methods, as they are found to fail or yield unstable solutions when the number of variables is large relative to the sample size. To tackle this issue, we propose a two-stage regularized approach for exploratory structural equation modeling. In the first stage, we introduce a novel (exploratory) approximate factor analysis technique that not only estimates the measurement model but also the factor scores; indeterminacy of the measurement model is addressed by imposing simple structure through regularizing techniques (LASSO penalty and cardinality constraint). The factor scores can then be used to estimate the structural model in the second stage. An extensive simulation shows that the proposed method outperforms other approaches in recovering the underlying simple structure of the measurement model in both low-dimension high-sample-size and high-dimension low-sample-size settings. The use of the method is demonstrated on two empirical datasets. An implementation of the proposed method in the R software is publicly available: https://github.com/trale97/regularizedESEM .