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09-11-2016 08:40 AM

Hello,

when I ran proc glimmix, I found the note "At least one element of the gradient is greater than 1e-3." in the log file and the output said:

The GLIMMIX Procedure

Iteration History

Objective Max

Iteration Restarts Evaluations Function Change Gradient

0 0 10 151.61524767 . 13.80694

1 0 13 145.29950034 6.31574732 4.078536

2 0 8 144.92020933 0.37929101 0.449007

4 1 120 144.91874425 0.00146509 0.031734

5 1 15 144.91872632 0.00001792 0.029066

6 1 31 144.91871078 0.00001554 0.050775

The convergence status is indeterminate.

However, the status variable in the convergence status table is 0 (i.e. successful optimization) with reason ''The convergence status is indeterminate." I am somewhat confused, because from my understanding, the status in the convergence table should not indicate successful optimization? Therefore I was wondering whether the estimates are reliable or not. And what I could do to prevent this indeterminate convergence status?

Thanks in advance and regards,

M

Accepted Solutions

Solution

09-14-2016
03:01 AM

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09-13-2016 03:19 PM

I performed a few experiments that might be useful to others:

1. If you remove the PARAM / LOWERB= statement, the some of the covariance estimates are negative and the estimated G matrix is not PD. I think this explains why the gradient isn't zero at the solution: the solution is not a local optimum but is a constrained optimum.

2. If you change the TECH= option in the NLOPTIONS statement, sometimes the problem converges and sometimes it doesn't. The problem converges for NEWRAP and QUANEW and doesn't give the mysterious "indeterminate status."

Good luck.

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09-12-2016 01:42 PM - edited 09-12-2016 01:43 PM

That is part of the output I have never seen before. I am curious to its origin. Could you please share your GLIMMIX code?

Steve Denham

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09-13-2016 01:44 PM

Thanks for your time! I also use SAS 9.4TS1M3 and ran the following code. Some sample data is attached

ods output ConvergenceStatus=cs;

proc glimmix data=data method= laplace;

class outcome predictor study;

model outcome(ref= "3")=predictor/ dist=multinomial link=glogit s cl;

random predictor /sub=study group=outcome G type= Chol;

nloptions maxiter=5000 tech=nrridg;

parms / lowerb=1e-4,.,1e-4,1e-4,., 1e-4;

freq count;

run;

Why does proc glimmix stop the optimization process at all? Thanks again!

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09-12-2016 04:29 PM

When the likelihood is maximized, all gradient values should be zero. Since we're dealing with an iterative optimization algorithm, exact zero is obviously not possible, so you're looking for the gradients to be close to zero. Of course, how close is "close" is anybody's guess. GLIMMIX sets a bar at 0.001, though there's nothing magical about it. So, as it says, the convergence in this is indeterminate since the biggest gradient value is bigger than that. That's not to say that the solution presented is bad. It just alerts you that you'll want to assess the resulting model.

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09-13-2016 08:52 AM

@StatDave_sas, I've seen the log note that at least one element of the gradient is greater than 1e-3 many times, but I have never seen the output statement 'The convergence status is indeterminate' before. I'm now running 9.4TS1M3, but have been using GLIMMIX ever since it became available.

Is there more to this story?

Steve Denham

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09-13-2016 09:19 AM

What model is being fit? What optimization method is being used? Without the SAS code (and possibly the data) there is no way to guess what is happening.

Solution

09-14-2016
03:01 AM

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09-13-2016 03:19 PM

I performed a few experiments that might be useful to others:

1. If you remove the PARAM / LOWERB= statement, the some of the covariance estimates are negative and the estimated G matrix is not PD. I think this explains why the gradient isn't zero at the solution: the solution is not a local optimum but is a constrained optimum.

2. If you change the TECH= option in the NLOPTIONS statement, sometimes the problem converges and sometimes it doesn't. The problem converges for NEWRAP and QUANEW and doesn't give the mysterious "indeterminate status."

Good luck.

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09-13-2016 03:50 PM

In case it helps, here is the result of PROC FREQ on the data. Notice that most of the observations are for outcome=1, with relatively few observations for outcome=2 and outcome=3. Notice also that these subsets have many cells with zero counts and that outcome=3 is used as the reference category.

proc freq data=ts.data;

tables outcome*predictor*study / nocum norow nocol nopercent;

weight count;

run;

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09-14-2016 03:06 AM

Exactly, I wanted the G Matrix to be p.d and did not realize that this might cause other trouble.

Thank all of you for your precious support!

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09-13-2016 03:31 PM

Just adding to Steve's comments. I have used GLIMMIX countless times, and have often dealt with convergence problems and problems with large parameter gradients at the solution. I've gotten all the standard warnings, but I don't recall ever seeing the message mentioned in the OP. I think something else is going on.