From sarkar at mail.utexas.edu  Thu Nov 17 02:22:20 2005
From: sarkar at mail.utexas.edu (sarkar@mail.utexas.edu)
Date: Thu, 17 Nov 2005 02:22:20 +0100 (CET)
Subject: [Rd] Principal Components Analysis (PR#8320)
Message-ID: <20051117012220.307D01E370@slim.kubism.ku.dk>

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



[Rd] Principal Components Analysis (PR#8320)
sarkar@mail.utexas.edu