Effects of Cross-loadings on Determining the Number of Factors to Retain

In exploratory factor analysis (EFA), cross-loadings frequently occur in empirical research, but its effects on determining the number of factors to retain are seldom known. In this paper, we analyzed whether and how cross-loadings affected the performance of the parallel analysis (PA), the empirical Kaiser criterion (EKC), the likelihood ratio test (LRT), the comparative fit index (CFI), the Tucker-Lewis index (TLI), and the root mean square error of approximation (RMSEA) in determining the number of factors to retain. A large-scale simulation study was also conducted. A few conclusions can be drawn: (1) overall, PA provides the most accurate performance, especially when data are non-normally distributed; (2) cross-loadings noticeably affect the performance of PA, CFI, and TLI with different patterns, and they virtually have no effect on EKC, LRT, and RMSEA; (3) no method is immune to the sizable detrimental effect of normality assumption violation. Several recommendations were provided.