Factor Analysis Revisited – How Many Factors are There?

Abstract

We suggest a procedure to improve the overall performances of several existing methods for determining the number of factors in factor analysis by using alternative measures of correlation: Pearson's, Spearman's, Gini's, and a robust estimator of the covariance matrix (MCD). We examine the effect of the choice of the covariance used on the number of factors chosen by the KG rule of one, the 80% rule, the Minimum average partial (MAP), and the Parallel Analysis Methodology (PAM). Extensive simulations show that when the entire (or part) of the data come from heavy-tail (lognormal) distributions, ranking the variables which come from non symmetric distributions improves the performances of the methods. In this case, Gini is slightly better than Spearman. The PAM and MAP procedures are qualitatively superior to the KG and the 80% rules in determining the true number of factors. A real example involving data on document authorship is analyzed.

Keywords:

• Correlation
• Factor analysis
• Principal components

Mathematics Subject Classification:

• 62H25

Acknowledgement

The authors thank Professor Cliff Spiegelman for consultations and for access to the word count data analyzed in this manuscript. We also thank an anonymous referee whose comments greatly improved the articles content and the presentation. The research was partially supported by the BGU Paul Ivanier Center for Robotics Research and Production Management.