Applying SEM, Exploratory SEM, and Bayesian SEM to Personality Assessments

Despite the importance of demonstrating and evaluating how structural equation modeling (SEM), exploratory structural equation modeling (ESEM), and Bayesian structural equation modeling (BSEM) work simultaneously, research comparing these analytic techniques is limited with few studies conducted to systematically compare them to each other using correlated-factor, hierarchical, and bifactor models of personality. In this study, we evaluate the performance of SEM, ESEM, and BSEM across correlated-factor, hierarchical, and bifactor structures and multiple estimation techniques (maximum likelihood, robust weighted least squares, and Bayesian estimation) to test the internal structure of personality. Results across correlated-factor, hierarchical, and bifactor models highlighted the importance of controlling for scale coarseness and allowing small off-target loadings when using maximum likelihood (ML) and robust weighted least squares estimation (WLSMV) and including informative priors (IP) when using Bayesian estimation. In general, Bayesian-IP and WLSMV ESEM models provided noticeably best model fits. This study is expected to serve as a guide for professionals and applied researchers, identify the most appropriate ways to represent the structure of personality, and provide templates for future research into personality and other multidimensional representations of psychological constructs. We provide Mplus code for conducting the demonstrated analyses in the online supplement.