Questions on Glimmix convergence and random level units

[lijunchen]

I have been using GLIMMIX to get the random effects estimates for second level units (counties). The data has over 40,000 level-1 records nested within 8 level-2 units (counties). The dependent variable is binary event indicator "event_pm" (1=event, 0=no event). There are no covariates except for county level random effect. The GLIMMIX program is shown below as well as the event frequencies for each level 2 county.

However, to my surprise, the model did not converge. Is it because 8 level-2 units is too few for the GLIMMIX model? Or is it because the number of events (event=1) for some counties are too few? One county has only over 30 events. What options can I use to overcome the non-convergence problem?

Any suggestions are appreciated.

PROC GLIMMIX data = ppage4 /*method=RSPL*/ noclprint pconv=1e-4;

   class county;

   model event_pm (event="1") =

         /dist=binary  solution;

     random intercept /subject=county solution cl;

run;

	Cumulative
county  event_pmFrequency	Frequency

------------------------------------------------

	1	0	6445	6445
	1	1	212	6657
	3	0	12436	19093
	3	1	376	19469
	5	0	1677	21146
	5	1	59	21205
	7	0	1216	22421
	7	1	36	22457
	9	0	12055	34512
	9	1	377	34889
	11	0	3855	38744
	11	1	116	38860
	13	0	1240	40100
	13	1	32	40132
	15	0	1673	41805
	15	1	50	41855

[lvm]

There can be many reasons for nonconvergence, and it would be not for the reason you are worried about. It is not clear if it is getting close to convergence (just needing more steps) or is stuck far from the solution locus. It could be stuck on the inner or outer iteration of the doubly iterative RSPL method. I suggest you increase the maximum number of iterations and try different optimization techniques. Add

nloptions maxiter=1000 maxfunc=1000 technique=NRRIDG;

Or try TRUREG or CONGRA for technique.

For binary data, you could also change your estimation to method=LAPLACE on the procedure statement. But this might be v-e-r-y slow with the number of levels you have.