[R] which to trust...princomp() or prcomp() or neither?

[Jari Oksanen]

Blair Smith <b.smith <at> irl.cri.nz> writes:

> 
> According to R help: 
> princomp() uses eigenvalues of covariance data.
> prcomp() uses the SVD method.
> 
> yet when I run the (eg., USArrests) data example and compare with my own 
> "hand-written" versions of PCA I get what looks like the opposite.
...clip...
> You see the problem: my SVD method yields results numerically similar to 
> the princomp() method which supposedly uses the eigenvector calculation.
> Whereas my eigenvector calculation method yields results numerically 
> similar to the prcomp() method which supposedly is a SVD calculation!
> 
> Also, it surprised me that the two methods would differ so markedly (only 2
significant 
> figure agreement at best).  Ultimately the question is which method to trust
as most 
> accurate?  
> 
> When I get time I'll just put in some data with KNOWN PC stdevs to see, but
I'm 
> still curious to see if any of you reading this help list could explain in
advance?
> 

Blair,

A behavioural test is not the best choice here: the source code is visible and
you can look there and see that prcomp() indeed uses svd() and princomp() uses
eigen(). The easiest way to dump the code is to write the name of the function
without trailing parentheses.

The differences in the numbers you cite has nothing to do with the underlying
algorithm, but it is only due to the scaling of the results: Function
princomp()uses divisor 'N' for the covariance matrix (this is explicitly
documented in?princomp), whereas prcomp() uses divisor 'N-1' (which is implied
in ?prcomp --
this really could be more explicit).

So you see: you did not need a guru to answer you -- reading the code and docs
was sufficient.

Cheers, Jari Oksanen