[R] R vs SPSS output for princomp

[James Howison]

Hi,

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?

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?

The full R commands and SPSS syntax follow below along with the
differing output.

Thanks, James
http://freelancepropaganda.com

R analysis
===========
I run:

 > library(mva)
 > DVfmla
~webeval1 + webeval2 + webeval3 + webeval4 + webeval5 + webeval6 +
     webeval7 + webeval8
 > loadings(DV.pca <- princomp(DVfmla, scale=T, cor=T))

Loadings:
          Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7 Comp.8
webeval1 -0.357  0.258 -0.202  0.458  0.629 -0.350  0.112 -0.159
webeval2 -0.340  0.510         0.255 -0.305  0.651  0.136 -0.143
webeval3 -0.319  0.316 -0.276 -0.797  0.244        -0.145
webeval4  0.247  0.633  0.681               -0.248
webeval5  0.391  0.150 -0.357 -0.183 -0.158 -0.185  0.584 -0.513
webeval6  0.392  0.252 -0.282  0.140               -0.756 -0.334
webeval7 -0.382  0.128 -0.162        -0.651 -0.596 -0.114  0.121
webeval8  0.377  0.268 -0.428  0.158                0.143  0.746

<snip SS loadings>

 >plot(DV.pca)  # This is exactly the same as the SPSS scree-plot.

SPSS Analysis
=============

FACTOR
   /VARIABLES webeval1 webeval2 webeval3 webeval4
              webeval5 webeval6 webeval7 webeval8
   /MISSING LISTWISE
   /ANALYSIS webeval1 webeval2 webeval3 webeval4
			webeval5 webeval6 webeval7 webeval8
   /PRINT INITIAL EXTRACTION
   /PLOT EIGEN
   /CRITERIA FACTORS(8) ITERATE(25)
   /EXTRACTION PC
   /ROTATION NOROTATE
   /METHOD=CORRELATION .

As mentioned the proportions of varience explained and the scree
plot are identical.  However SPSS produces this "Component Matrix"
which we, in class, have been calling "the loadings":

WEBEVAL1  -0.798  0.253  0.178  0.317 -0.370  0.167 -0.033 -0.037
WEBEVAL2  -0.764  0.487  0.026  0.188  0.186 -0.309 -0.108 -0.043
WEBEVAL3  -0.719  0.309  0.217 -0.564 -0.125 -0.040  0.043  0.052
WEBEVAL4   0.558  0.591 -0.563 -0.063 -0.029  0.131  0.030 -0.019
WEBEVAL5   0.864  0.161  0.313 -0.128  0.075  0.138 -0.221 -0.200
WEBEVAL6   0.876  0.252  0.237  0.100  0.008  0.017 -0.088  0.308
WEBEVAL7  -0.858  0.128  0.133  0.054  0.349  0.308  0.090  0.037
WEBEVAL8   0.847  0.256  0.316  0.111  0.000 -0.087  0.296 -0.094

Can anyone tell me why these are different (It seems likely that
this is a scaling of some kind as the SPSS ones just look to have
been made larger in some way).  Or is it that SPSS is reporting
cumulatively while R is not?

Thanks in advance,
James