Re: Re: st: factor analysis on tetrachoric correlation

[Richard Williams <Richard.A.Williams.5@nd.edu>]

At 09:59 PM 1/23/2004 +0100, Jean-Benoit Hardouin wrote:
> OK, I understand your proposition. Instead to use the matrix of the 
> tetrachoric correlations between my items, I used simulated dataset with a 
> correlation structure similar to this matrix.
>
> It's interesting, but I don't know if this could be valid !!
John Uebersax has a discussion on factor analysis with tetrachoric 
correlations and shows how to do it with various programs (Stata, alas, not 
being among them):

http://ourworld.compuserve.com/homepages/jsuebersax/irt.htm

Among other things, he says

"One may factor analyze the matrix of tetrachoric correlations just as one 
would a matrix of Pearson correlations. One can use any software that will 
estimate a common factor model. "

If I am following him correctly, the trick is deciding on the best 
estimation method given that you are analyzing tetrachoric 
correlations.  For example, he states

"Based on limited experience, I have found the PRINIT method [iterated 
principal factor analysis or IPFA] better for factoring tetrachorics than 
most other SAS factoring methods (a comparable method is available with 
SPSS). Knol and Berger found good results with this method, but suggested 
that unweighted least-squares estimation may be preferable in order to 
avoid possible "Heywood cases." (A Heywood case is an estimation problem 
where a commonality estimate becomes 1.0 or greater). "

My guess is that, if I wanted to clone Uebersax's suggested procedure for 
SAS using Stata, I would

(1) Compute the tetrachoric correlations using -tetrac- or another program
(2) Use -corr2data- to create a fake data set with the tetrachoric 
correlations (in SAS or SPSS, this wouldn't be necessary; I could just 
input the correlations directly)
(3) Run Stata -factor- with the -ipf- option (iterated principal factor method)

He also discusses how Lisrel can use a weighted least squares approach that 
requires the computation of both the tetrachoric correlations and the 
asymptotic variance/covariance matrix for estimated parameters, with the 
latter being used for the wls.  Perhaps if you could figure out how to 
compute these weights you could use the aweights option in Stata to clone 
what Lisrel does.

Again, I am just sort of guessing here; if possible, I would recommend 
taking a published paper with known results and see if you can replicate it 
with Stata.  (Better yet might be to use a program like SAS or Lisrel where 
it is documented how to do this, but that apparently is not an option.  I'm 
not familiar with all of the different estimation methods, but it appears 
some other programs offer more options and/or might make this easier than 
Stata does.)

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