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Re: st: RE: PCA, reverse scorings


From   Juan Julio Gutierrez <juanju@yahoo.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: RE: PCA, reverse scorings
Date   Sun, 30 Dec 2007 11:33:53 -0800 (PST)

Thanks Maarten and Jay, 

I have tried to follow Jay's suggestion "to pick reference items to fix the signs of the solution"
without luck. 

If you could provide guidance on this, it would be greatly appreciated. 

Thank you

Juan Julio 



--- "Verkuilen, Jay" <JVerkuilen@gc.cuny.edu> wrote:

> >>I am working on creating an index using PCA. 
> When running PCA the first time, with the original values the loadings
> come up with some unexpected signs<<
> 
> Principal components (and factor loadings) are arbitrary up to
> reflection. You have to pick reference items to fix the signs of the
> solution. As Maarten noted, you're getting exactly the same scores back.
> 
> 
> Jay
> 
> *
The two factors should be exactly the same. The original factor is
created using the folowing formula:

F1 = -0.51811*skillw + 0.5766*eduatt + 0.55153*rd + -0.30919*itexp	

The new factor is created using the following formula:

F2 = 0.51811*-1*skillw + 0.5766*eduatt + 0.55153*rd + 0.30919*-1*itexp

The two formulae are exactly the same.

-- Maarten

--- Juan Julio Gutierrez <juanju@yahoo.com> wrote:
> I am working on creating an index using PCA. 
> When running PCA the first time, with the original variable values,
> the loadings come up with some unexpected signs
> 
>  KI index loadings	
>  original variables	
> 
>  skillw	-0.51811
>  eduatt	0.576
>  rd	0.55153
>  itexp	-0.30919
>  
> I would expect that skillw and itexp would have positive values
> affecting the new variable I
> create with the command score (I am susing STATA 8). 
> 
> Reverse scoring: I have multiplied both variables (skillw and itexp)
> by -1 to get the opposite
> sign. the results now are: 
> 
>  KI index loadings	
>  	
>  newskillw	0.51811
>  eduatt	         0.576
>  rd	         0.55153
>  newitexp	0.30919
>   
> Now I get loadings that make sense. However when using the score
> command to save the loadings and
> listing the values, both new variables (i.e. w. original variables
> and with opposite sign) are
> exactly the same. 
>  
>  I would assume that the values should be different providing the
> different signs of the loadings.


-----------------------------------------
Maarten L. Buis
Department of Social Research Methodology
Vrije Universiteit Amsterdam
Boelelaan 1081
1081 HV Amsterdam
The Netherlands

visiting address:
Buitenveldertselaan 3 (Metropolitan), room Z434




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