Correlation Structures in Hierarchical Data Analysis Using PROC GLIMMIX vs. PROC GEE

[varatt90]

Hi all, 

I have a categorical variable with multiple unordered categories and am working with hierarchical data where clustering occurs at the hospital level. There is significant variance at the hospital level affecting my outcome, which is why I'm using PROC GLIMMIX instead of PROC GEE, as PROC GEE assumes an independent working correlation structure when you use a multinomial distribution.

My questions are:

1. Does the independent correlation structure in PROC GEE account for the nested data structure?
2. What correlation structure is assumed in PROC GLIMMIX, and does it adequately account for the nested data?

Here’s a sample of my code that I would like to run:

PROC GLIMMIX Data=Test Method=laplace;
CLASS hospitalid outcome (REF="0") year (REF="0") age (REF="0") sex (REF="0");
MODEL outcome = year age sex / DIST=multinomial LINK=glogit ALPHA=0.05 CL ODDSRATIO solution;
RANDOM Intercept / SUBJECT=hospitalid GROUP=outcome;
RUN;
 

[SteveDenham]

Your particular GLIMMIX code assumes separate variance components for each level of outcome, estimated from the various hospitals. This is the default for your RANDOM statement. For a multinomial, I think that is the only sensible structure, as imposing a correlation between levels for a generalized logit strikes me as a dangerous step toward convergence, Hessian and G matrix issues unless you have "close to homogeneous" responses across all of the subjects.

I'll call in @StatDave at this point. I think the assumption in PROC GEE that concerns you is no different than the default being fit by your code in GLIMMIX - that the variance components are interchangeable. If that is the case, i think GEE has a better chance of producing usable results.

SteveDenham