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Re: st: Aren't distinct factors from factor analysis or PCA orthogonal to each other?


From   Maarten buis <maartenbuis@yahoo.co.uk>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Aren't distinct factors from factor analysis or PCA orthogonal to each other?
Date   Mon, 17 Aug 2009 06:43:56 +0000 (GMT)

--- On Mon, 17/8/09, kokootchke wrote:
> I am new to factor analysis and I am trying to use it to
> decompose a big matrix of economic, financial, and political
> variables for many countries. So I run
> 
> factor var1-var100
> 
> and then I look that the first 3 factors explain most of
> the variation in that matrix, so then I want to use these
> three factors to see whether another variable (a measure of
> the "risk" of the country) is explained by these three
> factors. So I do:
> 
> predict factor1 factor2 factor3
> reg risk factor1 factor2 factor3
> 
> and I obtain very strongly significant estimates. 
> 
> My first question is: if I understand correctly, these
> factors should be orthogonal from each other. If that's the
> case, a regression such as:
> 
> reg risk factor1
> 
> should NOT give me a different coefficient for factor1
> compared to the factor1 coefficient in the first regression
> that includes all three factors, right? This is because if I
> omit factor2 and factor3, these things would go into the
> error term of my regression, but they wouldn't be adding any
> correlation between the error term and factor1, so the
> factor1 coefficient shouldn't change.
> 
> Or should I?
> 
> In my case, it does. Why is this, can you please help me
> understand?

This is definately true for principle components analysis: 

*------------- begin example --------------------
sysuse auto, clear
pca weight price rep78 turn length displacement
predict sc1 sc2 sc3
corr sc*
reg mpg sc*
reg mpg sc1
*-------------- end example ---------------------

The way I keep pca and factor analysis apart is that pca
is more "mechanical" (It finds orthogonal vectors) while
factor analysis is more "theoretical" (there is a latent
variable influencing the observed variables). I don't 
use either of these very often, so I need those simple
rules of thumb. Those who use it more often can 
probably say much more about this.

Hope this helps,
Maarten

-----------------------------------------
Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen
Germany

http://home.fsw.vu.nl/m.buis/
-----------------------------------------


      

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