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Re: st: Factor analysis after multiple imputation in STATA
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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