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st: RE: RE: Factor Analysis: which explained variance?


From   "Verkuilen, Jay" <JVerkuilen@gc.cuny.edu>
To   "'statalist@hsphsun2.harvard.edu'" <statalist@hsphsun2.harvard.edu>
Subject   st: RE: RE: Factor Analysis: which explained variance?
Date   Mon, 21 Dec 2009 13:53:50 -0500

Nick Cox wrote:

>P.P.S. the whole notion of variance is perhaps a little suspect when the
originals are indicator variables. <

@Nick: I don't know, you have variances, they're just functions of the mean (proportion)! However, there are covariances that aren't redundant.  

@The original poster:

With four indicators, you really can only afford a one dimensional factor analysis. Anything higher dimension will be, essentially, unidentified, and thus even more indeterminate than usual for factor analysis. Three indicators is exactly identified. Four indicators with correlated factors that have two indicators per factor is also identified, but if the solution says that you have three and one you're really out of luck. 

Without knowing the tetrachoric correlation matrix (these are indicators, i.e., binary, so polychoric is just tetrachoric anyhow) it's very hard to say on any statistical grounds. 

Is there a theoretical reason to form a sum score from these indicators? For instance, do they operate like items on a quiz where you want to know the total score? 

Jay

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