[R] Principal Component analysis question

[Damien Joly]

I have a question about princomp(mva) that I hope isn't too newbie.

I used the sample data from Table 1.1 in "Manly (1986/1994) Multivariate 
Statistical Methods: a primer. Chapman and Hall" on sparrow body 
measurements.

I rescaled the data to mean 0 and SD 1, and the covariance matrix is:

           V1        V2        V3        V4        V5
V1 1.0000000 0.7349642 0.6618119 0.6452841 0.6051247
V2 0.7349642 1.0000000 0.6737411 0.7685087 0.5290138
V3 0.6618119 0.6737411 1.0000000 0.7631899 0.5262701
V4 0.6452841 0.7685087 0.7631899 1.0000000 0.6066493
V5 0.6051247 0.5290138 0.5262701 0.6066493 1.0000000

Now when I call princomp [fun<-princomp(~V1+V2+V3+V4+V5)], I get the 
following loadings:

        Comp.1      Comp.2     Comp.3      Comp.4     Comp.5
V1 -0.4517989 -0.05072137  0.6904702  0.42041399 -0.3739091
V2 -0.4616809  0.29956355  0.3405484 -0.54786307  0.5300805
V3 -0.4505416  0.32457242 -0.4544927  0.60629605  0.3427923
V4 -0.4707389  0.18468403 -0.4109350 -0.38827811 -0.6516665
V5 -0.3976754 -0.87648935 -0.1784558 -0.06887199  0.1924341

However, this is in contrast to the results in Manly's book:

       Comp.1      Comp.2     Comp.3      Comp.4     Comp.5
V1 0.4517989 -0.05072137  0.6904702 -0.42041399  0.3739091
V2 0.4616809  0.29956355  0.3405484  0.54786307 -0.5300805
V3 0.4505416  0.32457242 -0.4544927 -0.60629605 -0.3427923
V4 0.4707389  0.18468403 -0.4109350  0.38827811  0.6516665
V5 0.3976754 -0.87648935 -0.1784558  0.06887199 -0.1924341

Interestingly, when I do the same in SAS, I get:

        Comp.1      Comp.2     Comp.3      Comp.4     Comp.5
V1  0.4517989  0.05072137 -0.6904702  0.42041399 -0.3739091
V2  0.4616809 -0.29956355 -0.3405484 -0.54786307  0.5300805
V3  0.4505416 -0.32457242  0.4544927  0.60629605  0.3427923
V4  0.4707389 -0.18468403  0.4109350 -0.38827811 -0.6516665
V5  0.3976754  0.87648935  0.1784558 -0.06887199  0.1924341

Finally, when I do it by "hand" in R (i.e., c<-cov(data); e<-eigen(c)), 
I get a fourth answer:

           V5          V4         V3          V2         V1
V1 0.4517989  0.05072137 -0.6904702 -0.42041399 -0.3739091
V2 0.4616809 -0.29956355 -0.3405484  0.54786307  0.5300805
V3 0.4505416 -0.32457242  0.4544927 -0.60629605  0.3427923
V4 0.4707389 -0.18468403  0.4109350  0.38827811 -0.6516665
V5 0.3976754  0.87648935  0.1784558  0.06887199  0.1924341


Can anyone point me in the right direction here?  I can email the raw 
data to anyone if that would help.

Thank you in advance...

Damien

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