[Jesper Eriksson]

Another question: Does not the result, shown above, after

 mixed Complication || Id:

 LR test vs. linear model: chibar2(01) = 0.00 Prob >= chibar2 = 1.0000

imply that a multilevel model does not provide a significantly better fit to the data than a single level model without random effects. In other words; I could skip using random effects on Id?

[Felix Bittmann]

Yes I agree, the random intercepts for ID are not useful here. Even the results for the hospital intercepts from model1 are not impressive. I think any of the following might suffice:

xtset hospital
xtlogit ...

Maybe you can just use a LPM (if the mean of complication is not too extreme) and go

areg ..., absorb(hospital) vce(robust)

[Jesper Eriksson]

Thank you Felix. I might even consider not using RE on Hospital. Many thanks for your help!