Exploratory structural equation modeling and the curse of dimensionality.

Area of Science:

• Behavioral Sciences
• Psychometrics
• Statistical Modeling

Background:

• Next-generation behavioral science research involves intensive data collection and complex models with many parameters relative to sample size.
• Traditional latent-variable methods struggle with large variable-to-sample size ratios, leading to unstable solutions.
• Existing methods face challenges in accurately estimating measurement and structural models under these conditions.

Purpose of the Study:

• To propose a novel two-stage regularized approach for exploratory structural equation modeling (ESEM).
• To address the limitations of traditional methods in handling high-dimensional data with small sample sizes in behavioral research.
• To enhance the stability and accuracy of latent-variable modeling in complex data scenarios.

Main Methods:

• A two-stage regularized approach for ESEM was developed.
• Stage one employs a novel exploratory approximate factor analysis with LASSO penalty and cardinality constraints to estimate the measurement model and factor scores.
• Stage two utilizes the estimated factor scores to determine the structural model.

Main Results:

• The proposed method demonstrated superior performance in recovering the underlying simple structure of the measurement model.
• Effectiveness was shown in both low-dimension high-sample-size and high-dimension low-sample-size settings.
• The method's utility was validated using two empirical datasets.

Conclusions:

• The novel two-stage regularized ESEM approach provides a robust solution for complex behavioral science data.
• This method enhances the estimation of measurement and structural models, particularly when dealing with large numbers of variables and limited sample sizes.
• An R software implementation is publicly available for broader application.