| Three computational solutions to the number of factors problem were investigated over a wide variety of typical psychometric situations using Monte Carlo simulated population matrices with known characteristics. The standard error scree, the minimum average partials test, and the technique of parallel analysis were evaluated head-to-head for accuracy. The question of using principal components-based eigenvalues versus common factors-based eigenvalues in the analyses was also investigated. As a benchmark, the commonly used eigenvalues-greater-than-one criterion was included. Across all conditions, the principal components-based version of parallel analysis was found to most accurately recover dimensionality using sample correlation matrices drawn from populations with known, simple factor structures. The high degree of accuracy observed for this method suggests that a workable solution to the age-old number of factors problem may be close at hand. |
