Exploratory structural equation modeling and the curse of dimensionality

Existing latent variable methods are found to fail or provide unstable solutions when the number of variables is large compared to the sample size. To tackle this issue,we propose a two-stage regularized least-squares approach for exploratory structural equation modeling. In the first stage, we introduce a novel exploratory 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. 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 sparse structure of the measurement model in both low-dimension high-sample-size and high-dimension low-sample-size settings. It also estimates the path coefficients of the structural model with low bias. An implementation of the proposed method in the R software is publicly available: https://github.com/trale97/RegularizedLSLV.