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

From   Maarten buis <>
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 L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen


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