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Re: Re: st: factor analysis on tetrachoric correlation


From   Richard Williams <[email protected]>
To   [email protected]
Subject   Re: Re: st: factor analysis on tetrachoric correlation
Date   Sat, 24 Jan 2004 11:02:18 -0500

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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