Applied Statistics Using SPSS, STATISTICA, MATLAB and R

336 8 Data Structure Analysis
using matrix x either as data matrix (icov ≠ 0) or as covariance matrix
(icov = 0).
The R eigen function behaves as the MATLAB eig function. For instance,
the eigenvalues and eigenvectors of Table 8.1 can be obtained with
eigen(cov(cbind(ART[1:50],PRT[1:50]))). The prcomp function
computes among other things the principal components (curiously, called
“rotation” or “loadings” in R) and their standard deviations (square roots of the
eigenvalues). For the dataset of Example 8.1 one would use:
> p p
Standard deviations:
[1] 117.65407 13.18348
Rotation:
PC1 PC2
[1,] 0.3500541 0.9367295
[2,] 0.9367295 -0.3500541
We thus obtain the same eigenvectors (PC1 and PC2) as in Table 8.1 (with an
unimportant change of sign). The standard deviations are the square roots of the
eigenvalues listed in Table 8.1. With the R princomp function, besides the
principal components and their standard deviations, one can also obtain the data
projections onto the eigenvectors (the so-called scores in R).
A scree plot (see section 8.2) can be obtained in R with the screeplot
function using as argument an object returned by the princomp function. The R
factanal function performs factor analysis (see section 8.4) of the data matrix x
returning the number of factors specified by factors with the specified
rotation method. Bartlett’s test scores can be specified with scores.
The R implemented functions pccorr and velcorr behave in the same way
as their MATLAB counterparts.
Figure 8.4. Partial view of STATISTICA specification window for principal
component analysis with standardised data.