Determining the number of factors using parallel analysis and its recent variants

Parallel analysis (PA) is recommended as one of the best procedures to determine the number of factors but its theoretical justification has long been questioned. The current study discussed theoretical issues on the use of eigenvalues for dimensionality assessment and reviewed the development of PA and its recent variants proposed to address the issues. The performances of 13 different PAs including PA with minimum rank factor analysis, revised PA, and comparison data method were investigated through a Monte Carlo simulation under a wide range of factor structures that produce small factor-representing and nonrepresenting eigenvalues for different types of measurement scales. Results showed that the traditional PA using full correlation matrices performed best in most of the conditions, especially when population error was involved. However, the overall accuracy of PA was not satisfactory when factor-representing eigenvalues were small, that is, when factor loadings were low and factor correlations were high. From these results, we suggest that the original PA be used to determine the number of factors but the estimated number should not be taken as a fixed estimate. The number of factors within ± 1 range of the estimate can be considered as viable candidates and interpretational validity of the competing models should be consulted for the decision.