Multivariate Analysis

  • W. N. Venables
  • B. D. Ripley
Part of the Statistics and Computing book series (SCO)


Multivariate analysis is concerned with datasets which have more than one response variable for each observational or experimental unit. The datasets can be summarized by data matrices X with n rows and p columns, the rows representing the observations or cases, and the columns the variables. The matrix can be viewed either way, depending whether the main interest is in the relationships between the cases or between the variables. Note that for consistency we represent the variables of a case by the row vector x.


Covariance Matrix Linear Discriminant Analysis Mahalanobis Distance Canonical Correlation Analysis Iris Data 
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  1. 1.
    A divisor of n — 1 is more conventional, but princomp calls coy . wt , which uses n .Google Scholar
  2. 2.
    In S we would use (1: 150)[duplicated(“paste”, data.frame(ir)))]Google Scholar
  3. 3.
    A corrected version of biplot . princomp from our library is used.Google Scholar
  4. 4.
    actually, this needs a modification to pltree . agnesGoogle Scholar
  5. 5.
    This will not work in earlier versions of S-PLUS (3.2 and 3.3).Google Scholar
  6. 6.
    with a Bartlett correction: see Bartholomew (1987, p. 46) or Lawley & Maxwell (1971, pp. 35–36). For a Heywood case (as here) Lawley & Maxwell (1971, p. 37) suggest the number of degrees of freedom should be increased by the number of variables with zero uniqueness.Google Scholar
  7. 7.
    This is a vector x such that original variable j was divided by xJ .Google Scholar
  8. 8.
    Bartholomew gives both covariance and correlation matrices, but these are inconsistent. Neither are in the original paper.Google Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • W. N. Venables
    • 1
  • B. D. Ripley
    • 2
  1. 1.Department of StatisticsUniversity of AdelaideAdelaideAustralia
  2. 2.University of OxfordOxfordEngland

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