How to do glimmix model with nominal (unordered) outcome?

[AprilS]

I am trying to fit a multinomial logistic model with random effects (ID is the cluster) and a 3-level nominal outcome, the outcome is not ordinal. I used SAS code like below:

   proc glimmix;
      class ID outcome;
      model outcome(ref=first) = explanatory/
                      dist=multinomial 
                      link=glogit;
      random intercept / subject=ID group=outcome;
   run;

But the model did not work and said G matrix is not positive definite. I tried glogit model several times with different outcomes and clusters, it either runs out of memory or has other issues. I wonder if I did anything wrong or there is a better way to do this kind of models in SAS?

[StatDave]

You could instead try fitting a GEE model:

proc gee;
      class ID;
      model outcome(ref=first) = explanatory/
                      dist=mult link=glogit;
      repeated subject=ID;
   run;

[AprilS]

Thanks! I tried this too, but it runs forever. Not sure if it is because of my computer or this model is too complex?  

[StatDave]

Like all modeling procedures, the time and memory needed increases with the number of parameters in the model. So, you might want to start with a small model (few predictors) and see if you can build up to a suitable model. Note that the number of parameters will increase dramatically as the number of levels of the response increases. So, if there are many response levels, you might consider a modified response that merges categories into fewer levels.

[AprilS]

Thanks, the response just has 3 levels and I only used one predictor with 2
levels, the sample size is about 500. Then I guess it is just because of
the computer power? Besides the computer power, I am curious if there is
any statistical computation method which might help?

Thanks again!

[StatDave]

So, you really just have an Sx2x3 table, where S is the number of subjects. For that, you can use a nonmodel-based approach. You could use the CMH statistics in PROC FREQ with your subject variable as the stratifying variable. For example, if your 2 level predictor is X and your 3 level response is Y:

proc freq;
table s*x*y/cmh noprint;
run;

The second CMH statistic tests if X and Y are associated. See the discussion in the FREQ documentation for details.