Please do RTFM: ?princomp says
Note:
The signs of the columns of the loadings and scores are arbitrary,
and so may differ between different programs for PCA, and even
between different builds of R.
and ?prcomp has a similar comment. Equally, the signs of eigenvectors are
arbitrary, and ?eigen says
Recall that the eigenvectors are only defined up to a
constant: even when the length is specified they are still
only defined up to a scalar of modulus one (the sign for real
matrices).
If you don't know why these are true, please ask your advisors for help.
On Thu, 17 Nov 2005 [EMAIL PROTECTED] wrote:
> Full_Name: Sahotra Sarkar
> Version: 2.2.0
> OS: Windows XP Professional
> Submission from: (NULL) (146.6.130.180)
>
>
> The following two commands should give the same results for the eigenvectors
> but
> do not (there is a sign reversal for the first one):
>
>> summary(princomp(bumpus),loading = TRUE)
> Importance of components:
> Comp.1 Comp.2 Comp.3 Comp.4 Comp.5
> Standard deviation 6.2801653 2.4285636 1.13995042 0.560733747 0.03458915
> Proportion of Variance 0.8399662 0.1256084 0.02767525 0.006696272 0.00002548
> Cumulative Proportion 0.8399662 0.9655746 0.99324988 0.999946156 0.99997164
> Comp.6 Comp.7 Comp.8 Comp.9
> Standard deviation 3.025628e-02 1.405339e-02 1.147326e-02 9.339938e-03
> Proportion of Variance 1.949623e-05 4.206121e-06 2.803451e-06 1.857837e-06
> Cumulative Proportion 9.999911e-01 9.999953e-01 9.999981e-01 1.000000e+00
>
> Loadings:
> Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7 Comp.8 Comp.9
> V1 0.497 0.851 0.171
> V2 0.853 -0.515
> V3 0.149 0.103 -0.965 0.189
> V4 -0.180 -0.981
> V5 -0.288 0.568 0.327 0.693
> V6 -0.399 0.565 0.154 -0.705
> V7 -0.867 -0.475 -0.107
> V8 0.352 -0.926 0.118
> V9 0.994
>> eigen(cov(bumpus))
> $values
> [1] 3.973263e+01 5.941610e+00 1.309113e+00 3.167514e-01 1.205271e-03
> 9.222233e-04
> [7] 1.989606e-04 1.326107e-04 8.788062e-05
>
> $vectors
> [,1] [,2] [,3] [,4] [,5]
> [1,] -0.496897319 0.8505093640 0.171388489 0.018744742 -0.0002708851
> [2,] -0.852790441 -0.5152155401 0.081515933 0.025301353 0.0031275939
> [3,] -0.149011771 0.1032588064 -0.965116017 0.188813583 0.0029039523
> [4,] -0.059981091 0.0228574697 -0.180065518 -0.981007482 0.0301789269
> [5,] -0.002474454 -0.0009781164 -0.003402721 -0.011404980 -0.2884751568
> [6,] -0.002255070 -0.0003234929 -0.002776659 -0.014386855 -0.3990284747
> [7,] -0.003505091 -0.0005603692 -0.006526439 -0.022328724 -0.8671382015
> [8,] -0.001124313 0.0005858447 -0.003031985 -0.006957916 -0.0674635788
> [9,] -0.003810707 0.0004531193 -0.006127501 -0.009908937 -0.0122192249
> [,6] [,7] [,8] [,9]
> [1,] -0.001028476 1.638253e-06 0.0004887328 -0.0003561342
> [2,] -0.002350593 -8.313864e-04 -0.0003929312 0.0005026715
> [3,] -0.004636198 8.031165e-05 0.0015963693 0.0010649875
> [4,] -0.011239114 -5.568762e-03 0.0035062479 0.0003785351
> [5,] 0.083901242 5.675807e-01 0.3265320650 -0.6934139460
> [6,] 0.032231827 5.646388e-01 0.1541661011 0.7049350072
> [7,] -0.058318858 -4.748060e-01 -0.1070487286 -0.0849487969
> [8,] 0.014813290 3.516922e-01 -0.9260185177 -0.1182046449
> [9,] 0.994055719 -9.937481e-02 -0.0249932592 0.0324567705
>
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>
--
Brian D. Ripley, [EMAIL PROTECTED]
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
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