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st: RE: Interpreting PCA output


From   "Verkuilen, Jay" <JVerkuilen@gc.cuny.edu>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: Interpreting PCA output
Date   Fri, 25 Jul 2008 13:21:22 -0400

Mona Mowafi wrote:

>>I'm new to the list and hope you will be able to help me with an
analysis problem before me.  I have conducted a principal components
analysis to identify principal components for 67 underlying indicators
or household asset.  The first principal component is clearly important,
but in fact, according to commonly used "rule of 1", so are the rest of
the first 20 principal components.<<  

It's not good to speak ill of the dead, but the "rule of 1" is something
I hope Henry Kaiser is rolling a mite uneasily in his grave about
("Little Jiffy" is another). At minimum you should look into parallel
analysis, which uses a better cutoff line based on applying PCA to
simulated independent data with the same number of variables. 


>>Using a scree test, I may choose to only use the first 5 principal
components.  But in any case, I am not sure how one is supposed to
interpret the 2nd, 3rd, 4th, etc eigenvectors from the output.

You probably can't. They are probably nuisance eigenvectors, caused by
nonlinearity or the fact that PCA assumes errorless variables. 


>>I am interested ultimately in using this information to make a
household asset index.  Below is output for the pca and the first 6
eigenvectors; any guidance is truly appreciated...<<

First of all, you probably want factor analysis, not PCA for what you're
doing. Presuming you have a decent sample size (um, say 500 or so),
maximum likelihood factor analysis followed by an oblique rotation will
be best. (Unfortunately Stata doesn't have minres/ULS factor analysis.
If you need more flexibility, download the free CEFA from Michael
Browne's web page:
http://faculty.psy.ohio-state.edu/browne/software.php. If CEFA doesn't
do it, it probably shouldn't be done at all.) 

Might I suggest getting your hands on a copy of Lattin, Carroll and
Green (2003), Analyzing Multivariate Data, Duxbury Press? It has nice
chapters on PCA, EFA and CFA, all written in a readable style. 

JV

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