[R] prcomp help: is this a typo?

Prof Brian D Ripley ripley at stats.ox.ac.uk
Fri Jun 16 08:10:18 CEST 2000


On Thu, 15 Jun 2000, Ramon Diaz-Uriarte wrote:

> Dear All,
> 
> The help for prcomp, under "Value" says:
> 
>     sdev: the standard deviation of the principal components (i.e., the
>           eigenvalues of the cov matrix, though the calculation is
>           actually done with the singular values of the data matrix).
> 
> The way I read it, it implies that the sdev are the eigenvalues, but  I think
> that sdev is actually the square root of the eigenvalues ( from looking at,
> say, pp. 317 and 318 in Morrison's (1990) "Multivariate statistical methods" or
> pp. 61 to 63 of Krzanowski's (1990) "Principles of multivariate analysis"; or by
> comparing the output of 
> > prcomp(my.data,  scale = TRUE)
> 
> with the brute force
> 
> > eigen(cor(my.data))
> )

Take a look at 1.1.0.  That has been altered to be

    sdev: the standard deviations of the principal components (i.e.,
          the square roots of the eigenvalues of the
          covariance/correlation matrix, though the calculation is
          actually done with the singular values of the data matrix).

Thank you for pointing it out.  As your example show, the correlation
matrix is appropriate if scale.=TRUE. (And if center=FALSE it is an
uncentred cov/cor matrix.)

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272860 (secr)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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