I see that Robin has already responded about the basic nature of the problem here. Let me just add the following observations about Ryan's specific problem.

Ryan has two levels of random effects: city (N~=40) and person within city (N~=2500 or N~=62/city). The random effects design matrix requires a column for each city random effect (intercept, month, and disease*x1 as specified in the model). In addition, the design matrix includes more than 60 columns of person within city random effects. I don't know how the GLIMMIX procedure is constructed - whether the design matrix for the person random effects is reduced as much as possible so that the number of columns in the person effects portion of the design is represented as the number of persons in the city that has the most individuals (something over 62) or whether the design is represented with 2500 columns and thus 2500 random effects. I would hope that it is the former.

Regardless, the quadrature solution requires integrating over all of the random effects which means at a minimum there would be 3 + (62+) nested integrals. The computation problem becomes immense here. Following Robin's post, there would be at least 3**(65) likelihood evaluations per iteration.

While the GLIMMIX procedure does in theory support estimation of nested random effect models when a quadrature solution has been requested, in practice this is limited to models with a suitably small design matrix. The data employed here do not have a suitably small design matrix for the random effects. Thus, I see no hope of fitting this model using quadrature methods.

Finally, let me post another thought or two about the model which is fit here. There appear to be four disease classes, but disease was not named on the CLASS statement. That seems wrong to me. I would also echo Robin's concerns regarding month parameterization (class vs continuous). I also have questions regarding whether month and disease*x1 should be named on the random statement.

I might take exception to Robin's suggestion to ignore the person random effects and focus only on the city random effects. If anything, I would remove the city random effects and specify only the person random effects. There is probably more variability in the person random effects than in the city random effects. You want to account for the main source of random variation. Thus, it would seem to me that you would want to model the person random effects. When the city random effects have been excluded, the person random effects will include city variability. But the reverse is not true. When persons are excluded, then their random effects are averaged over and will almost certainly average to something quite close to zero within a city - especially when there are so many persons/city.

Thus, I would suggest dropping the city random effects and estimate the model with just person random effects. The nesting problem that causes expansion of the random effect design matrix disappears when city is dropped from the model. You should be able to fit the person random effect model with more quadrature points (although if month and disease*x1 are kept as random effects and especially if month and disease have been added to the CLASS statement, then the model could once again expand beyond what can reasonably be handled with a large number of quadrature points).

Dale

--------------------------------------- Dale McLerran Fred Hutchinson Cancer Research Center mailto: dmclerra@NO_SPAMfhcrc.org Ph: (206) 667-2926 Fax: (206) 667-5977 ---------------------------------------

--- On Wed, 11/12/08, Robin R High <rhigh@UNMC.EDU> wrote:

> From: Robin R High <rhigh@UNMC.EDU> > Subject: Re: Insufficient Resources to Perform Adaptive Qaudrature... > To: SAS-L@LISTSERV.UGA.EDU > Date: Wednesday, November 12, 2008, 8:06 AM > Ryan, > > Terms or images to express the "infinite" have > long been a part of our > history: > > From Genesis 15, God speaks to Abram "Look toward > heaven and count the > stars, if you are able to count them." Then he said to > him, "So shall your > descendants be." > > ...in the early 80s it was "Cosmos" and Carl > Sagan's famous phrase > "billions and billions..." > > .. and to match wits, when "infinity" looks at > us, we react with the > desire for "more POWER, EH, EH!" (Tim the > Toolman) > > .. and now the new SAS 9.2 generation can speak of > "infinity" through > "random effects with quadrature", though I > imagine that Abram or the > "Cosmos" audience would produce a blank stare if > such terminology had been > in vogue. > > So, after that digression, please read the section on > quadrature/laplace > options in > > http://www2.sas.com/proceedings/forum2007/177-2007.pdf > > from which the following section is extracted: > > ***begin quote > proc glimmix method=quad(qpoints=5); > class A B id; > model y = / dist=negbin; > random A / subject=id; > run; > > Computing the marginal log likelihood requires the > numerical evaluation of > a four-dimensional integral. As > part of this evaluation, 54 = 625 conditional log > likelihoods need to be > computed per observation on each > pass through the data. Now suppose that an additional > random effect with b > = 2 levels is added and the > previous RANDOM statement becomes the following: > > random A A*B / subject=id; > > For each observation, this now requires evaluation of > 5**(4+8) = > 244,140,625 [commas added for clarity] conditional log > likelihoods on each > pass through the data. > ***end quote > > .. whatever "each pass" actually means, remember > that GLIMMIX needs to > iterate and reiterate to find a solution, which I suppose > like the > national debt or "bailout" figures we've been > hearing gets rather large > fairly quickly. I suppose this is one reason that I once > recall hearing > Oliver S. himself say that he was reluctant to include quad > as an option > with GLIMMIX (though it is nice to now be able to produce > the same results > with GLIMMIX that one would produce with NLMIXED). > > So, in my opinion, don't hestitate to work with other > estimation routines, > esp. when you have a reasonably large sample size (which > you do) and the > random effects aren't too "big". > > And finally, just a few thoughts about your code, one can > always start > with a simpler model and work up in complexity, if > possible. And I'm > curious why is month treated as a linear covariate, esp. > one treated as > having a random slope within each city? Perhaps quarterly > for a seasonal > categorical effect might be a suggestion. And the following > code would > likely capture the essence of the problem, though with > binary data it may > be computationally difficult to estimate random subject > effects, even > though conceptually it would be important. > > proc glimmix data=mydata ; > class Person_ID City_ID; *include month or a quarterly > effect here?? ; > model y = Disease x1 month disease*x1 / s dist=binary; > random intercept x1 / subject=City_ID ; * would a > type=<another option> > work better? ; > run; > > .. as always, something new to learn or features to > consider,esp. now with > 9.2 available... > > Robin High > UNMC > > Note: not sure why the original message became garbled when > I look at it > on the SAS-L archives, so thought I would re-submit > hopefully with this > version of the note now in an ungarbled format. > > > > > > Ryan <Ryan.