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

Area of Science:

• Psychometrics
• Quantitative Psychology
• Statistical Modeling

Background:

• General factor modeling is increasingly popular for understanding complex data structures.
• Assessing the reliability of general factor scores is crucial for accurate interpretation.
• Omega hierarchical estimation is a key metric, but its approximation via modern methods is under-explored.

Purpose of the Study:

• To compare the performance of six algorithms in approximating omega hierarchical estimates.
• To investigate how different structural complexities (bi-factor, second-order, cross-loadings) affect estimation.
• To provide guidance on selecting appropriate algorithms for omega hierarchical estimation in exploratory factor analysis.

Main Methods:

• Six algorithms were evaluated: Bi-quartimin, bi-geomin, Schmid-Leiman (SL), SLiD, DSL, and DBF.
• Monte-Carlo simulations were employed, incorporating bi-factor and second-order structures with varying complexities.
• Re-analysis of eight classical datasets was conducted to validate simulation findings.

Main Results:

• The SLiD algorithm consistently provided the best approximation of omega hierarchical across most simulated conditions.
• Schmid-Leiman (SL), bi-quartimin, and bi-geomin algorithms showed unsatisfactory recovery of omega hierarchical.
• Direct SL (DSL) and Direct Bi-Factor (DBF) performance was contingent on the discrepancy between general and group factor loadings.

Conclusions:

• Algorithm selection significantly impacts the accuracy of omega hierarchical estimation.
• SLiD emerges as a recommended algorithm for approximating omega hierarchical in complex factor structures.
• Researchers should carefully consider the chosen algorithm and data structure when interpreting omega hierarchical reliability.