Yes, you can obtain predicted values from the GLIMMIX procedure. However, it is probably not quite as easy to write the code in GLIMMIX because you need to write an ESTIMATE statement for every subject. Thus, you would need code like the following:
ods output Estimates=Predictions;
proc glimmix data=xxx;
class q03;
model q327 = q103r / dist=binary;
random q03;
estimate "Prediction for 1st subject"
intercept 1
q103r 59
| q03 1 /
ilink;
estimate "Prediction for 2nd subject"
intercept 1
q103r 59
| q03 0 1 /
ilink;
...
estimate "Prediction for 10th subject"
intercept 1
q103r 59
| q03 0 0 0 0 0 0 0 0 0 1 /
ilink;
...
estimate "Prediction for 20th subject"
intercept 1
q103r 59
| q03 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 /
ilink;
...
run;
Note that each estimate statement specifies the same linear combination of the fixed effects but picks up a different column of the random effect q03. We need a separate ESTIMATE statement for each level of q03. In addition, in order to predict the expected probability value (rather than eta), we need the ILINK option on each ESTIMATE statement.
Note, too, the use of the vertical bar (|) before the random effect q03 in ESTIMATE statement. The vertical bar indicates that the terms which follow are found in the random effects structure.
Additionally, it should be observed that you will not get the same results out of the ESTIMATE statement if you specify the RANDOM statement as
random intercept / subject=r03;
The GLIMMIX procedure makes model specification much easier than does the NLMIXED procedure. However, obtaining predicted values conditional on levels of the random effects is considerably easier in NLMIXED.