> Does anyone know whether or not STATA can calculate the shares of
> variation in a principal component attributable to its underlying
> variables, or, if STATA cannot do this directly, how to calculate these
> given STATA's output from the "score" command and/or the eigenvectors?
As far as I understand, those would be the squares of the factor loadings.
. pca mpg wei leng
(obs=74)
(principal components; 3 components retained)
Component Eigenvalue Difference Proportion Cumulative
------------------------------------------------------------------
1 2.70121 2.45616 0.9004 0.9004
2 0.24504 0.19130 0.0817 0.9821
3 0.05375 . 0.0179 1.0000
Eigenvectors
Variable | 1 2 3
-------------+--------------------------------
mpg | -0.55448 0.83165 0.03013
weight | 0.58965 0.36707 0.71943
length | 0.58726 0.41667 -0.69391
So, the proportion due to mpg is 0.55448^2 = 0.307, etc.
Stata does not save them, so you need to think about ways around it using
the spectral commands Stata has:
. mat accum Cov = mpg wei leng, dev nocons
(obs=74)
. mat li Cov
symmetric Cov[3,3]
mpg weight length
mpg 2443.4595
weight -264948.11 44094178
length -7483.5135 1195077.3 36192.662
. mat Corr = corr(Cov)
. mat li Corr
symmetric Corr[3,3]
mpg weight length
mpg 1
weight -.80717486 1
length -.79577944 .94600864 1
. mat symeigen X V = Corr
. mat li V
V[1,3]
e1 e2 e3
r1 2.7012074 .24504411 .05374846
. mat li X
X[3,3]
e1 e2 e3
mpg -.55447516 .83165484 .03012519
weight .58964667 .36706509 .71943035
length .58725983 .41666948 -.69391097
Now you can access the eigenvalues in the matrix V, and the eigenvectors
(aka factor loadings) in the matrix X.
This is pretty much what Stata does for -pca-, but it formats this stuff
somewhat nicer :)).
--- Stas Kolenikov
-- Ph.D. student in Statistics at UNC-Chapel Hill
- http://www.komkon.org/~tacik/ -- [email protected]
* This e-mail and all attachments to it are not intended to provide any
* reasonable point of view and was transmitted to you in error. It
* should be immediately deleted by all recipients unless they really
* enjoy communicating with the author :). Other restrictions apply.
*
* For searches and help try:
* http://www.stata.com/support/faqs/res/findit.html
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/
