09-18-2015 11:21 AM
When using proc GEE or proc GENMOD with WEIGHT option the covariance of Yi is given by : Vi = phi Ai1/2 Wi1/2 R(alpha) Wi1/2 Ai1/2.
Then the used estimating equation is sum Di Vi-1 (Yi-mui)=0.
However, the correct formula given by Robins 1995 is sum Di Vi-1 Wi (Yi-mui)=0.
I agree that when we choose an independence correlation structure it is equivalence. However, it may be different if we use an exchangeable correlation structure. I found an article by Lin et Rodriguez 2014 stating that the estimation may even be biased in some case. They claim that it may had been corrected in version 13.2 of SAS. But I cannot find any difference at least in the documentation of the procedures. Do anyone have any insight?
Also, Is there any superiority advantage of using Vi = phi Ai1/2 Wi1/2 R(alpha) Wi1/2 Ai1/2 ?
Thank you very much,
09-23-2015 03:30 PM - edited 09-23-2015 03:32 PM
The Robins method is one of the weighted GEE methods in PROC GEE. See "Weighted Generalized Estimating Equations under the MAR Assumption : Observation-Specific Weighted GEE Method" in the Details section of the GEE documentation.
10-07-2015 11:55 PM
Thanks for this reference.
However, do you have any insight why it had been implemented Vi = phi Ai1/2 Wi1/2 R(alpha) Wi1/2 Ai1/2 and not Vi = phi Ai1/2R(alpha) Ai1/2 Wi at the very beginning?
Thanks you very much,
10-08-2015 09:31 AM
First of all, note that:
Vi = phi Ai1/2 Wi1/2 R(alpha) Wi1/2 Ai1/2
Is incorrect. The actual decomposition of the covariance matrix (using your notation) is:
Vi = phi Ai1/2 Wi(-1/2) R(alpha) Wi(-1/2) Ai1/2
As for why it is decomposed like that, the answer really has to do with the way linear algebra works, and it is difficult to give a full answer here (since, as far as I know, these forums don't support LaTeX). I'd recommend asking that question over at CrossValidated where someone can walk you through the algebra.