Comparing Exploratory Structural Equation Modeling and Existing Approaches for Multiple Regression with Latent Variables

Abstract

Exploratory structural equation modeling (ESEM) is an approach for analysis of latent variables using exploratory factor analysis to evaluate the measurement model. This study compared ESEM with two dominant approaches for multiple regression with latent variables, structural equation modeling (SEM) and manifest regression analysis (MRA). Main findings included: (1) ESEM in general provided the least biased estimation of the regression coefficients; SEM was more biased than MRA given large cross-factor loadings. (2) MRA produced the most precise estimation, followed by ESEM and then SEM. (3) SEM was the least powerful in the significance tests; statistical power was lower for ESEM than MRA with relatively small target-factor loadings, but higher for ESEM than MRA with relatively large target-factor loadings. (4) ESEM showed difficulties in convergence and occasionally created an inflated type I error rate under some conditions. ESEM is recommended when non-ignorable cross-factor loadings exist.

Keywords:

• exploratory structural equation modeling
• latent variables
• Monte Carlo simulation
• multiple regression

Notes

¹ Since ${\lambda }_T$ and ${\lambda }_C$ are standardized factor loadings of each of the indicators $x_1\sim x_6$ on the correlated latent variables ${\xi }_1$ and ${\xi }_2$, respectively, ${\lambda }_T^2+{\lambda }_C^2+2\rho {\lambda }_T{\lambda }_C\le 1$ is a restriction to be satisfied. Given $\rho =.3$, the restriction is not satisfied when ${\lambda }_T=.95$ and ${\lambda }_C=.20$ or $.25$.

Additional information

Funding

This research was funded by grants from the National Natural Science Foundation of China (31771245), the Graduate Research Fellowship Program of South China Normal University (2012kyjj106), the U.S. Department of Education (R305D140037), and National Science Foundation (1461355).