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# Clear understaning of hessian matrix in Proc mixed/glimmix

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 !!!

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‎08-06-2014 07:41 AM
Posts: 2,655

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

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

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Solution
‎08-06-2014 07:41 AM
Posts: 2,655

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

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

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