Structured Factor Analysis: A Data Matrix-Based Alternative Approach to Structural Equation Modeling

Joreskog's covariance-based approach (JCA) has been considered a standard method for structural equation modeling. However, JCA is prone to the occurrence of improper solutions and cannot make probabilistic inferences about the true factor scores. To address the enduring issues of JCA, we propose a data matrix-based alternative, termed structured factor analysis (SFA). Given a data matrix of indicators, SFA begins by estimating both measurement model parameters and factor scores by minimizing a single cost function via an alternating least squares algorithm, which mathematically guarantees convergence to proper solutions. It then employs the factor score estimates to estimate structural model parameters. Once all parameters are estimated, SFA further estimates the probability distribution of the factor scores that can generate the data matrix of indicators, which can be used for probabilistic inferences about the true factor scores. We investigate SFA's performance and empirical utility through simulated and real data analyses.

Automated summary

JCA is a standard method for structural equation modeling but often leads to improper solutions and lacks probabilistic inference for true factor scores. To address these issues, we propose SFA, a data matrix-based alternative that minimizes a cost function to estimate parameters and factor scores and enables probabilistic inference.