Parallel analysis (PA) assesses the number of factors in exploratory factor analysis. Traditionally PA compares the eigenvalues for a sample correlation matrix with the eigenvalues for correlation matrices for 100 comparison datasets generated such that the variables are independent, but this approach uses the wrong reference distribution. The proper reference distribution of eigenvalues assesses the kth factor based on comparison datasets with k−1 underlying factors. Two methods that use the proper reference distribution are revised PA (R-PA) and the comparison data method (CDM). We compare the accuracies of these methods using Monte Carlo methods by manipulating the factor structure, factor loadings, factor correlations, and number of observations. In the 17 conditions in which CDM was more accurate than R-PA, both methods evidenced high accuracies (i.e.,>94.5%). In these conditions, CDM had slightly higher accuracies (mean difference of 1.6%). In contrast, in the remaining 25 conditions, R-PA evidenced higher accuracies (mean difference of 12.1%, and considerably higher for some conditions). We consider these findings in conjunction with previous research investigating PA methods and concluded that R-PA tends to offer somewhat stronger results. Nevertheless, further research is required. Given that both CDM and R-PA involve hypothesis testing, we argue that future research should explore effect size statistics to augment these methods.
The Sample Covariance Matrix and the Sample Correlation Matrix and Their Applications in the Sample Principal Component
