On Omega Hierarchical Estimation: A Comparison of Exploratory Bi-Factor Analysis Algorithms

As general factor modeling continues to grow in popularity, researchers have become interested in assessing how reliable general factor scores are. Even though omega hierarchical estimation has been suggested as a useful tool in this context, little is known about how to approximate it using modern bi-factor exploratory factor analysis methods. This study is the first to compare how omega hierarchical estimates were recovered by six alternative algorithms: Bi-quartimin, bi-geomin, Schmid-Leiman (SL), empirical iterative empirical target rotation based on an initial SL solution (SLiD), direct SL (DSL), and direct bi-factor (DBF). The algorithms were tested in three Monte-Carlo simulations including bi-factor and second-order structures and presenting complexities such as cross-loadings or pure indicators of the general factor and structures without a general factor. Results showed that SLiD provided the best approximation to omega hierarchical under most conditions. Overall, neither SL, bi-quartimin, nor bi-geomin produced an overall satisfactory recovery of omega hierarchical. Lastly, the performance of DSL and DBF depended upon the average discrepancy between the loadings of the general and the group factors. The re-analysis of eight classical datasets further illustrated how algorithm selection could influence judgments regarding omega hierarchical.