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RE: st: RE: PCA, reverse scorings

From   "Verkuilen, Jay" <[email protected]>
To   <[email protected]>
Subject   RE: st: RE: PCA, reverse scorings
Date   Sun, 30 Dec 2007 16:46:14 -0500

Well it's really a substantive issue. Pick one or more items based on their wording. Assume the following six item questionnaire was used:

I love cats.
Cats are my favorite animal.
Cats are great! 
If I have to choose a pet it wouldn't be a cat.
Cats are the spawn of satan.
The best cat is a dead cat.

Responses on a 1 to 7 agreement scale.  

Obviously the first three items will be positively correlated as will the second three. We would expect the blocks of variables to be negatively correlated. There should be one dominant component and maybe a smaller one or two due to nonlinearity, method factor, etc.   

Depending on the algorithm used a PCA or factor analysis may assign negative signs to the first block of items or the second set---the choice is arbitrary. You can freely multiply the entire vector of loadings by -1 without changing anything, which simply flips the direction of the scale from cat liking to cat disliking. 


-----Original Message-----
From: [email protected] on behalf of Juan Julio Gutierrez
Sent: Sun 12/30/2007 2:33 PM
To: [email protected]
Subject: Re: st: RE: PCA, reverse scorings 
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" <[email protected]> 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 <[email protected]> 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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