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Re: st: Factor analysis after multiple imputation in STATA


From   Jeff <stat3@jp.pair.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Factor analysis after multiple imputation in STATA
Date   Sun, 22 Jul 2007 13:10:12 -0500

At 11:27 AM 7/17/2007, you wrote:
As a side note, I think that Rubin (1987)'s formula applied to factor
analysis would simply be the mean of the of the factor loadings across
the imputed datasets (I have 5 imputed datasets) , but is this
correct, or should I be using a different formula for the factor
loadings across imputed datasets?

I would greatly appreciate any assistance,

Woolton

I'm working on something similar so this is of interest to me.

...hoping that someone could clarify something. My understanding (which is admittedly limited) is that the application of the actual em algorithm for the purpose of missing data imputation results in parameter estimates that are already unbiased and essentially the same as you would get through using Rubin's rules to combine/average the parameter estimates obtained through using multiple imputed data sets obtained through some type of procedure like data augumentation. ...and that the purpose of MI (relative to straight EM) is simply to adjust the standard errors so that they are proper and account for the uncertainty of imputation process. ...and that FIML generally does not provide adjustment to standard errors when there are missing data by default in most software - at one point the AMOS website acknowledged this and provided a calculator that was useful to properly adjust the standard errors when FIML was used in the presence of missing data. I don't know if this was fixed in later versions of Amos.

If I'm correct (and again, I'm not sure I am), you would need to only apply some procedure that uses the EM algorithm to impute a single data set that would subsequently provide factor loadings that were essentially the same as those obtained through the use of multiple imputation, since the EM procedure doesn't add the noise to each data set that represents the imputation uncertainty that the MI procedures do.

...again, however, I'm hoping that someone could either confirm that I'm correct, or tell me where I'm wrong because I'm working on something similar.

Jeff


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