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Principal Component Analysis and Factor Analysis

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Abstract

Principal component analysis has often been dealt with in textbooks as a special case of factor analysis, and this tendency has been continued by many computer packages which treat PCA as one option in a program for factor analysis—see Appendix A2. This view is misguided since PCA and factor analysis, as usually defined, are really quite distinct techniques. The confusion may have arisen, in part, because of Hotelling’s (1933) original paper, in which principal components were introduced in the context of providing a small number of ‘more fundamental’ variables which determine the values of the p original variables. This is very much in the spirit of the factor model introduced in Section 7.1, although Girschick (1936) indicates that there were soon criticisms of Hotelling’s method of PCs, as being inappropriate for factor analysis. Further confusion results from the fact that practitioners of ‘factor analysis’ do not always have the same definition of the technique (see Jackson, 1981). The definition adopted in this chapter is, however, fairly standard.

Keywords

  • Principal Component Analysis
  • Factor Loading
  • Factor Model
  • Multivariate Normality
  • Factor Number

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 1986 Springer Science+Business Media New York

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Jolliffe, I.T. (1986). Principal Component Analysis and Factor Analysis. In: Principal Component Analysis. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-1904-8_7

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  • DOI: https://doi.org/10.1007/978-1-4757-1904-8_7

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4757-1906-2

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