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

From   kokootchke <>
To   statalist <>
Subject   st: Aren't distinct factors from factor analysis or PCA orthogonal to each other?
Date   Mon, 17 Aug 2009 00:46:34 -0400

Hello, guys. 

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?

My second question is: I have tried to sign all of my variables, var1-var100, so that an increase in each variable represents an improvement in economic conditions.

In that case, if my first regression shows negative estimates for factor1, 2, and 3, would it be fair to interpret these coefficients as "an improvement in economic conditions reduces the risk?"

Thanks a lot.

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