Convergence criterion (GCONV=1E-8) satisfied. At least one element of the gradient is greater 1e-3

[Maya1]

Hello,

in my multinomial logistic regression with proc glimmix, I frequently get the following note:

NOTE: Convergence criterion (GCONV=1E-8) satisfied.
NOTE: At least one element of the gradient is greater than 1e-3.

In the convergence status table, I find status=0 with reason= 'Convergence criterion (GCONV=1E-10) satisfied.'

From the paper http://support.sas.com/resources/papers/proceedings12/332-2012.pdf

and a previous post (https://communities.sas.com/t5/SAS-Procedures/MEANING-Convergence-criterion-GCONV-1E-8-satisfied/m-p...), I learned that the relative change in the gradient value is sufficiently small (due to a maximum/ minimum/ saddle point in the objective function),  but the gradient value itself is not be small. So I followed the recommendation in the paper and set nloptions / gconv=0. However, the note "At least one element of the gradient is greater than 1e-3." persists but now the convergence status table says 'The convergence status is indeterminate.' with status=0. If I choose gconv= 1e-10, I still get the note in the log file and the convergence status table again says 'The convergence status is indeterminate.'

So my question is: Do I have to worry about the note or which impact does it have? And what else could I try?

Thanks in advance and kind regards.

M

[SteveDenham]

In almost all of the cases I have worked with, I have seen the same NOTE and haven't been terribly concerned.  However, it could easily lead to very large standard errors for the associated parameter.  This can sometimes be handled by doing the following:

What you might do is add the ITDETAILS option to your PROC GLIMMIX statement, and see which element of the gradient is still relatively large.  If you then relate that back to a model parameter, you could attempt to rescale the associated variable.  As ide from this, things like altering the optimization technique in an NLOPTIONS statement could be tried--ridging often helps, so tech=NRRIDG might be a good start.

Steve Denham

[Maya1]

Thanks, Mr Denham! Is there any literature which I could cite that this issue is not a big deal and that only the standard errors might be affected?

Btw, I already use tech=nrridge in combination with method=laplace and have only one binary predictor and count data as dependent variable, so I guess, rescaling is not an option? Anything else that I could try?

Thanks again, M

[SteveDenham]

Could you report the results of the ITDETAILS, along with your model?  That might help.

As far as a read, Walt Stroup's Generalized Linear Mixed Models would be my choice. Also, check for posts by @lvm--he has mentioned a couple of papers by Stroup that may touch on this as well.

Steve Denham