[R] R vs SPSS output for princomp

[Prof Brian Ripley]

On Mon, 5 May 2003, James Howison wrote:

> I am using R to do a principal components analysis for a class
> which is generally using SPSS - so some of my question relates to
> SPSS output (and this might not be the right place).  I have
> scoured the mailing list and the web but can't get a feel for this.
> It is annoying because they will be marking to the SPSS output.
> 
> Basically I'm getting different values for the component loadings
> in SPSS and in R - I suspect that there is some normalization or
> scaling going on that I don't understand (and there is plenty I
> don't understand).  The scree-plots (and thus eigen values for each
> component) and Proportion of Variance figures are identical - but
> the factor loadings are an order of magnitude different.  Basically
> the SPSS loadings are much higher than those shown by R.
> 
> Should the loadings returned by the R princomp function and the
> SPSS "Component Matrix" be the same?

Only if they are defined the same.  The length of a PCA loading is 
arbitrary.  R's are of length (sum of squares of coefficients) one:
how are SPSS's defined?

> And subsidiary question would be:  How does one approximate the
> "Kaiser's little jiffy" test for extracting the components (SPSS
> by default eliminates those components with eigen values below 1)?
> I've been doing this by loadings(DV.prcomped)[,1:x] after inspecting
> the scree plot (to set x) - but is there another way?

eigen values of what exactly?  The component sdev is the aquare roots of
the eigenvalues of the (possibly scaled) covariance matrix: maybe you
intend this only for a correlation matrix?

In R you have the source code, so if you know what you want you can find 
the pieces.

-- 
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 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595