topic Clear understaning of hessian matrix in Proc mixed/glimmix in SAS Programming

Clear understaning of hessian matrix in Proc mixed/glimmix

kaushal2040 — Mon, 04 Aug 2014 21:47:22 GMT

Hello forum,

I am using proc mixed with follow code.

Proc mixed data=test;

class diet drug pup_id rat_id;

model tg=diet drug diet*drug/ ddfm=bw;

random int/ sub=pup_id(rat_id);

run;

When I remove ddfm=bw, the hessian matrix is not positive defnite.

Can someone explain anout hessian matrix, positive defiteness, and algorithm involved in it?

Thanks !!!

Re: Clear understaning of hessian matrix in Proc mixed/glimmix

SteveDenham — Wed, 06 Aug 2014 11:41:03 GMT

The Hessian matrix is a matrix of partial second derivatives of the objective function. If it is positive definite (all positive eigenvalues) then the point is a local minimum. The idea behind maximum likelihood is to find the point where this occurs. For more on this, check out the Details>Mixed Models Theory in the PROC MIXED documentation. From there, you can find references to texts that go into this in much more detail.

Steve Denham