[R] prcomp eigenvalues

[Sundar Dorai-Raj]

Rebecca Young wrote:
> Hello,
> 
> Can you get eigenvalues in addition to eigevectors using prcomp?  If so how?
> I am unable to use princomp due to small sample sizes.
> Thank you in advance for your help!
> Rebecca Young
> 


Hi, Rebecca,

 From ?prcomp:

      The calculation is done by a singular value decomposition of the
      (centered and possibly scaled) data matrix, not by using 'eigen'
      on the covariance matrix.  This is generally the preferred method
      for numerical accuracy. ...

So you can get the singular values, but not the eigenvalues. You could 
use ?princomp if you really want the eigenvalues. In either case, you 
read the code to see how this is done.

x <- matrix(rnorm(1000), 100, 10)

# eigenvalues
v <- cov.wt(x)
ev <- eigen(v$cov * (1 - 1/v$n.obs), symmetric = TRUE)$values
ev[ev < 0] <- 0
princomp(x)$sdev
sqrt(ev)

# singular values
sv <- svd(scale(x, center = TRUE, scale = FALSE), nu = 0)
prcomp(x)$sdev
sv$d/sqrt(max(1, nrow(x) - 1))

HTH,

--sundar