Evaluating Factor Retention in Large Factor Analysis Models: A Simulation Study Comparing 15 Methods

Abstract

Exploratory factor analysis (EFA) is widely used to identify latent structures measured by observed indicators. Nevertheless, determining the number of factors remains a methodological challenge, especially when the size of the EFA model is large (e.g., models with more than 10 indicators per factor and more than five factors). This study evaluated the performance of 15 factor-retention methods under large factor analysis models, including parallel analysis (PA) using the mean and 95th percentiles of threshold, exploratory graph analysis (EGA) with GLASSO and TMFG estimations, sequential χ², fit indices (Comparative Fit Index [CFI], Tucker–Lewis Index [TLI], Root Mean Square Error of Approximation [RMSEA]), Kaiser Criterion (K1 rule), the very simple structure (VSS) method, the comparison data (CD) approach, the minimum average partial (MAP) test, the Hull method using the comparative fit index, Cattell’s acceleration factor criteria, and Bayesian information criterion (BIC). Specifically, we manipulated the number of factors (5, 6, and 7), indicators per factor (10 and 15), sample sizes (100, 200, 500, 800, 1,000, 1,500, 2,000, and 4,000), inter-factor correlations (.30, .50, and .70), and factor loadings (.40 and .70). Results reveal that PA-M and EGA-TMFG are the most robust methods across varying conditions. PA-M excels under low-to-moderate inter-factor correlations, while EGA-TMFG is more accurate in high-correlation scenarios when sample sizes are sufficient. Notably, EGA-Glasso may fail to converge when sample size is insufficient in large factor models.