The Performance of ESEM and BSEM in Structural Equation Models with Ordinal Indicators
Xinya Liang, Yanyun Yang, Chunhua Cao
Abstract
Recent developments allow for incorporating exploratory features into structural equation models (SEM). Two approaches, exploratory SEM (ESEM) and Bayesian SEM (BSEM), have been shown flexible of estimating complex SEM. This simulation study compared the performance of ESEM and BSEM for estimating structural regression models with ordinal indicators where cross-loadings were present in selected factors. Data were generated under conditions including various categorical data distributions, similarity of categorical distributions across indicators, and sample sizes. ESEM with Geomin rotation and BSEM with four small-variance normal priors on cross-loadings were used. Results indicated that ESEM may be prioritized over BSEM when sample sizes were large, distributions of ordinal indicators were symmetric or moderately asymmetric, and cross-loadings were non-ignorable. When sample sizes were relatively small, we recommend using one approach to complement the other. For BSEM, a sensitivity test is recommended to evaluate the impact of various prior choices on the estimation outcomes.