If I understand your question correctly, I think you can use the OUTPUT statement in PROC GLIMMIX and the PREDICTED keyword to get what you want. See this recent related post about visualizing fitted mixed models.  Assuming that you want to model the response as a multinomial proportion, you can specify DIST=MULT on the MODEL statement to fit a multinomial model. The Getting Started example describes a lot of the syntax, although the example is for a logistic model (two classes) instead of your three-class multinomial model. ... View more