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Evaluating Factor Retention in Large Factor Analysis Models: A Simulation Study Comparing 15 Methods
1University of Illinois Urbana-Champaign, USA.
Educational and Psychological Measurement
|June 29, 2026
Summary
Determining the correct number of factors in exploratory factor analysis (EFA) is challenging for large models. Parallel analysis (PA) and exploratory graph analysis (EGA) methods show robust performance across various conditions.
Area of Science:
- Psychometrics
- Statistical Modeling
- Data Analysis
Background:
- Exploratory Factor Analysis (EFA) is crucial for identifying latent structures.
- Determining the optimal number of factors is a significant methodological challenge, particularly in large-scale EFA models.
- Existing factor retention methods vary in performance depending on model characteristics.
Purpose of the Study:
- To evaluate the performance of 15 distinct factor-retention methods within large EFA models.
- To identify the most robust and accurate methods for determining the number of factors under diverse conditions.
- To provide empirical evidence to guide the selection of appropriate factor-retention techniques.
Main Methods:
- Evaluated 15 factor-retention methods, including Parallel Analysis (PA), Exploratory Graph Analysis (EGA) with GLASSO and TMFG, sequential chi-squared, fit indices (CFI, TLI, RMSEA), Kaiser Criterion, VSS, CD, MAP, Hull, Cattell's acceleration criteria, and BIC.
- Manipulated key parameters: number of factors (5-7), indicators per factor (10-15), sample sizes (100-4000), inter-factor correlations (.30-.70), and factor loadings (.40-.70).
Main Results:
- Parallel Analysis using the mean (PA-M) and Exploratory Graph Analysis with TMFG estimation (EGA-TMFG) demonstrated the highest robustness across tested conditions.
- PA-M performed best under low-to-moderate inter-factor correlations.
- EGA-TMFG showed superior accuracy in high-correlation scenarios with adequate sample sizes.
- EGA-Glasso exhibited convergence issues with insufficient sample sizes in large models.
Conclusions:
- PA-M and EGA-TMFG are recommended as reliable methods for factor retention in large EFA models.
- The choice between PA-M and EGA-TMFG may depend on the expected level of inter-factor correlation and available sample size.
- Researchers should be cautious when using EGA-Glasso with limited sample sizes in complex factor structures.
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