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

[kornbrot <d.e.kornbrot@herts.ac.uk>]

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

Is it possible to hierarchical EFA in stata?
Are there do  files?
Best
diana


On 17/08/2009 07:43, "Maarten buis" <maartenbuis@yahoo.co.uk> wrote:

> --- 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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Professor Diana Kornbrot
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