[R] factor analysis (pca): how to get the 'communalities'?

[Wolfgang Lindner]

Dear expe-R-ts,

I try some test data for a factorAnalysis (resp. pca) in the sense of Prof. 
Ripley's MASS § 11.1, p. 330 ff., just to prepare myself for an analysis of my 
own empirical data using R (instead of SPSS).

1. the data.

## The test data is (from the book of Backhaus et al.: Multivariate ## 
Analysemethoden. Springer 2000 [9th ed.], p. 300 ff):

a<-c(4.5,5.167,5.059,3.8,3.444,3.5,5.25,5.857,5.083,5.273,4.5)
b<-c(4.0,4.25,3.824,5.4,5.056,3.5,3.417,4.429,4.083,3.6,4.0)
c<-c(4.375,3.833,4.765,3.8,3.778,3.875,4.583,4.929,4.667,3.909,4.2)
d<-c(3.875,3.833,3.438,2.4,3.765,4.0,3.917,3.857,4.0,4.091,3.9)
e<-c(3.25,2.167,4.235,5.0,3.944,4.625,4.333,4.071,4.0,4.091,3.7)
f<-c(3.75,3.75,4.471,5.0,5.389,5.250,4.417,5.071,4.25,4.091,3.9)
g<-c(4.0,3.273,3.765,5.0,5.056,5.5,4.667,2.929,3.818,4.545,3.6)
h<-c(2.0,1.857,1.923,4.0,5.615,6.0,3.25,2.091,1.545,1.6,1.5)
i<-c(4.625,3.75,3.529,4.0,4.222,4.75,4.5,4.571,3.75,3.909,3.5)
j<-c(4.125,3.417,3.529,4.6,5.278,5.375,3.583,3.786,4.167,3.818,3.7)

m<-data.frame(a,b,c,d,e,f,g,h,i,j)

2. My try of a pca with R.

## My R input was:

m
cor(m)
library(mva)
m.pca<-princomp(m,cor=T)
m.pca
summary(m.pca)
loadings(m.pca)
m.pca$scores
m.FA <- factanal(factors = 3, covmat=cov(m))
m.FA

3. Here are my questions. 

Q1. 
The cor(m)-Matrix is the same as reported by using SPSS (or OpenStats2). 
But in R I get other eigenvalues compared with the following SPSS output:

Original matrix trace =  10,00
Roots (Eigenvalues) Extracted:
   1  5,052
   2  1,771
   3  1,427
   4  0,819
   5  0,430
   6  0,247
   7  0,159
   8  0,062
   9  0,029
  10  0,003

- What is going behind the scene? 
- Or what I am doing wrong in my use of R?
- If I am doing the pca correct, can I use the R results as equally aceptable 
  without further discussion? 
  Maybe a different 'hidden' algorithm is the reason for different results?

Q2. How to get the so called 'Communality Estimates' with R?

Here the values reported by SPSS for the above test data.frame m:
Communality Estimates as percentages:
  1 88,619
  2 76,855
  3 89,167
  4 85,324
  5 76,043
  6 84,012
  7 80,223
  8 92,668
  9 63,297
 10 88,786

Any help, suggestions or hints are very welcome.
Best regards and happy new year for you and R

Wolfgang

--
Wolfgang Lindner                           Lindner at math.uni-duisburg.de
   Gerhard-Mercator-Universitaet Duisburg  Tel: +49 0203 379-1326
   Fakultaet 4 - Naturwissenschaften       Fax: +49 0203 379-2528
   Institut fuer Mathematik,  LE 424
   Lotharstr. 65
   D 47048  Duisburg (Germany)