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help for ^pca^                                                   (STB-37: smv7)
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Principal components analysis
-----------------------------

   ^pca^ varlist [^if^ exp] [^in^ range] [weight] [^, f^actor^(^#^) s^td ^l^evel^(^#^)^ ]


^pca^ shares the features of all estimation commands; see [U] Chapter 26.

^pca^ typed without arguments redisplays previous estimation results.

To reset problem-size limits, see help @matsize@.


Description
-----------

^pca^ computes asymptotic standard errors of principal components for covariance
and correlation matrices and the percentage of explained variance. The 
computations are based on the assumption that the data is multivariate 
normally distributed. It is known that the estimates may be sensitive to 
violations of the normality assumption, and so these asymptotic results should 
be interpreted cautiously.

In a later version, I may replace the normal-based approximations (due to
Anderson 1963) with the asymptotic results for general sperical distributions 
due to Tyler (1981).


Options
-------

^factor(^#^)^ specifies the number of factors (components) to be extracted.

^std^ specifies that the pca analysis should be performed on the correlation
    matrix rather than on the covariance matrix. The reported standard 
    errors are not fully asymptotically correct for correlation matrices.

^level(^#^)^ specifies the confidence level, in percent, for confidence
    intervals.  The default is ^level(95)^ or as set by ^set level^.


Examples
--------

   . ^pca x1-x10^
   . ^pca x1-x10, fa(2) std^


References
----------

Anderson, T. W. (1963)  Asymptotic Theory for Principal Components Analysis.
    Annals of Mathematical Statistics. 34: 468-488.

Kshirsagar, A. M. (1972)  Multivariate Analysis. New York: Marcel Dekker. 
    See p 454 for asymptotic distribution of "percentage-explained".

Tyler, D. E. (1981) Asymptotic Inference for Eigenvectors. Annals of 
    Statistics, 9: 725-736.


Author
------

     Jeroen Weesie
     Utrecht University
     Netherlands
     weesie@@weesie.fsw.ruu.nl


Also see
--------

    STB:  STB-37 smv7
 Manual:  [R] factor
On-line:  help for @factor@