Principal Components, Factors and Correspondence Analysis

  • J. D. Jobson
Part of the Springer Texts in Statistics book series (STS)


In exploratory studies, researchers often include as many variables as possible to ensure that no relevant variables will be omitted. The resulting data matrices can sometimes be large and difficult to analyze, particularly if the level of correlation among the variables is high. In techniques such as multiple regression and discriminant analysis, variable selection procedures can be employed as a data reduction technique; however this method can result in the loss of one or more important dimensions. An alternative approach is to use all of the variables in X to obtain a smaller set of new variables that can be used to approximate X. The new variables are called principal components or factors and are designed to carry most of the information in the columns of X. The higher the level of correlation among the columns of X the fewer the number of new variables required. The techniques of principal components analysis and factor analysis are examples of data reduction techniques.


Correspondence Analysis Multiple Correspondence Analysis Factor Analysis Model Total Inertia Robust Principal Component Analysis 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Cited Literature and References

  1. 1.
    Andersen, Erling B. (1990).The Statistical Analysis of Categorical Data.Berlin: Springer-Verlag.zbMATHCrossRefGoogle Scholar
  2. 2.
    Bernstein, Ira H. (1987).Applied Multivariate Analysis.New York: Springer-Verlag.Google Scholar
  3. 3.
    Conway, Delores A. and Reinganum, Marc R. (1988). “Stable Factors in Security Returns: Identification Using Cross-Validation,”Journal of Business and Economic Statistics6, 1–15.Google Scholar
  4. 4.
    Everitt, B.S. (1984).An Introduction to Latent Variable Models.London: Chapman and Hall.zbMATHCrossRefGoogle Scholar
  5. 5.
    Gibbons, D.I., McDonald, G.C. and Gunst, R.F. (1987). “The Complementary Use of Regression Diagnostics and Robust Estimation,”Naval Research Logistics34, 109–131.zbMATHCrossRefGoogle Scholar
  6. 6.
    Giffi, A. (1990).Nonlinear Multivariate Analysis.New York: John Wiley and Sons.Google Scholar
  7. 7.
    Gorsuch, R.L. (1983).Factor AnalysisSecond Edition. Hillsdale, NJ: Lawrence Erlbaum.Google Scholar
  8. 8.
    Greenacre, M.J. (1984).Theory and Applications of Correspondence Analysis.New York: Academic Press.zbMATHGoogle Scholar
  9. 9.
    Hakistan, A.R., Rogers, W.T. and Cattell, R.B. (1982). “The Behavior of Number-of-Factors Rules with Simulated Data,”Multivariate Behavioral Research17, 193–219.CrossRefGoogle Scholar
  10. 10.
    Harman, H.H. (1976).Modern Factor AnalysisThird Edition. Chicago: University of Chicago Press.Google Scholar
  11. 11.
    Hawkins, D.M. (1980).Identification of Outliers.London: Chapman and Hall.zbMATHGoogle Scholar
  12. 12.
    Jackson, J. Edward (1990).A User’s Guide to Principal Components.New York: John Wiley and Sons.Google Scholar
  13. 13.
    Jambu, Michel (1991).Exploratory and Multivariate Data Analysis.New York: Academic Press.zbMATHGoogle Scholar
  14. 14.
    Jobson, J.D. (1988). Comment on “Stable Factors in Security Returns: Identification Using Cross-Validation,” by Conway and ReinganumJournal of Business and Economic Statistics6, 16–20.CrossRefGoogle Scholar
  15. 15.
    Jobson, J.D. and Schneck, Rodney (1982). “Constituent Views of Organizational Effectiveness: Evidence From Police Organizations.”Academy of Management Journal25, 25–46.CrossRefGoogle Scholar
  16. 16.
    Johnson, Richard A. and Wichern, Dean W. (1988).Applied Multivariate Statistical AnalysisSecond Edition. Englewood Cliffs, NJ: Prentice-Hall.zbMATHGoogle Scholar
  17. 17.
    Jolliffe, I.T. (1986).Principal Component Analysis.New York: Springer-Verlag.Google Scholar
  18. 18.
    Lawley, D.N. and Maxwell, A.E. (1971).Factor Analysis as a Statistical MethodSecond Edition. London: Butterworth and Company.zbMATHGoogle Scholar
  19. 19.
    Lebart, L, Morineau, A. and Warwick, K.M. (1984).Multivariate Descriptive Statistical Analysis.New York: John Wiley and Sons.zbMATHGoogle Scholar
  20. 20.
    MacDonnell, W.R. (1902). “On Criminal Anthropometry and the Identification of Criminals,”Biometrika1, 177–227.CrossRefGoogle Scholar
  21. 21.
    Mardia, K.V., Kent, J.T. and Bibby, J.M. (1979).Multivariate Analysis.London: Academic Press.zbMATHGoogle Scholar
  22. 22.
    Maxwell, A.E. (1977).Multivariate Analysis in Behavioral ResearchLondon: Chapman and Hall.Google Scholar
  23. 23.
    Morrison, Donald F. (1976).Multivariate Statistical MethodsSecond Edition. New York: McGraw-Hill.zbMATHGoogle Scholar
  24. 24.
    Mulaik, Stanley A. (1972).The Foundations of Factor Analysis.New York: McGraw-Hill.Google Scholar
  25. 25.
    Nishisato, S. (1980).Analysis of Categorical Data Dual Scaling and Its Application. Toronto: University of Toronto Press.Google Scholar
  26. 26.
    Seber, G.A.F. (1984).Multivariate Observations.New York: John Wiley and Sons.zbMATHCrossRefGoogle Scholar
  27. 27.
    Stevens, James (1986).Applied Multivariate Statistics for the Social Sciences. Hillsdale, NJ: Lawrence Erlbaum Associates.zbMATHGoogle Scholar
  28. 28.
    Theil, Henri (1971).Principles of Econometrics.New York: John Wiley and Sons.zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • J. D. Jobson
    • 1
  1. 1.Faculty of BusinessUniversity of AlbertaEdmontonCanada

Personalised recommendations