st: Degrees of Freedom, F-test and Multiple Imputation

[Andrea Bennett <mac.stata@gmail.com>]

Hi!

I am slightly confused with the degrees of freedom
in regressions based on imputed data (M=20). 
Let's say I have 50 school classes nested in 30 schools.

Assume a regression that is based on a single imputed 
data set (e.g. m=5) and clustered on the class-level.
Now, adding fixed effects for schools shows that the 
F-test has not enough degrees of freedom to be calculated.

However, running the same regression with the full set of 
imputed data (m=0, …, m=20) is - according to Stata - 
no problem since the degrees of freedom are calculated 
over the full range of all imputed observations.

My question: Can I belief these Stata calculations? I don't 
quite understand why I should have more degrees of 
freedom and whether I can make use of it, i.e. would it 
be statistically ok to include fixed effects in the above
case when working with the complete set of 
imputed data (m=0, …, m=20) since Stata reports 
the F-test just fine?

Your suggestions are very welcomed!

Andrea



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