On Closeness Between Factor Analysis and Principal Component Analysis Under High-Dimensional Conditions

  • L. Liang
  • K. HayashiEmail author
  • Ke-Hai Yuan
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 140)


This article studies the relationship between loadings from factor analysis (FA) and principal component analysis (PCA) when the number of variables p is large. Using the average squared canonical correlation between two matrices as a measure of closeness, results indicate that the average squared canonical correlation between the sample loading matrix from FA and that from PCA approaches 1 as p increases, while the ratio of p/N does not need to approach zero. Thus, the two methods still yield similar results with high-dimensional data. The Fisher-z transformed average canonical correlation between the two loading matrices and the logarithm of p is almost perfectly linearly related.


Canonical correlation Factor indeterminacy Fisher-z transformation Guttman condition Large p small N Ridge factor analysis 



Ke-Hai Yuan's work was supported by the National Science Foundation under Grant No. SES-1461355. The authors are grateful to comments from Drs. Sy-Miin Chow and Shin-ichi Mayekawa that led to significant improvements of the article.


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© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of PsychologyUniversity of Hawaii at ManoaHonoluluUSA
  2. 2.Department of PsychologyUniversity of Notre DameNotre DameUSA

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