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.)
*
* For searches and help try:
* http://www.stata.com/support/faqs/res/findit.html
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/
