topic Re: WARNING: The final Hessian matrix is full rank but has at least one negative eigenvalue in Statistical Procedures

WARNING: The final Hessian matrix is full rank but has at least one negative eigenvalue

Abbas_Arkawazi — Fri, 09 Jul 2021 18:24:53 GMT

Hello,
I am working on fitting nonlinear mixed model to my data using proc nlmixed.
My model has four fixed effects & five random effects.

But when I run the program, I get the following warning:

WARNING: The final Hessian matrix is full rank but has at least one
negative eigenvalue.
Second-order optimality condition violated.

Please help me solve this problem and guide me to the right way to solve this problem.

My code is the following and the data is in the attachment:

proc import datafile='C:\Users\Abbas Arkawazi\Desktop\test.xlsx'
DBMS =xlsx Out=test;
run;
proc nlmixed data=test ;
 parms b0=1 b1=2 b2=3  b3=4  a=2  b=1  aa=3  bb=1  s=100;
   m =b0+(b1*age)+(b2*creatin)+(b3*gender);
   y=urea;
   if status_u=1 then  f=((aa*bb*a*b)/s)*(exp(-b*exp((y-m)/s)))*((1-exp(-b*exp((y-m)/s)))**(a-1))*((((1-exp(-b*exp((y-m)/s)))**a)**(aa-1))/((1-((1-exp(-b*exp((y-m)/s)))**a))**(aa+1)))*((1+((((1-exp(-b*exp((y-m)/s)))**a)/(1-((1-exp(-b*exp((y-m)/s)))**a)))**aa))**(-bb-1)) ;
   else f= 1-((1+(((1-exp(-b*exp((y-m)/s)))**a)/(1-(1-exp(-b*exp((y-m)/s)))**a))**aa)**-bb)  ;
   ll=log(f);
   model y ~ general(ll);
run;

Re: WARNING: The final Hessian matrix is full rank but has at least one negative eigenvalue

PaigeMiller — Fri, 09 Jul 2021 19:18:23 GMT

https://communities.sas.com/t5/SAS-Procedures/Likelihood-in-PROC-NLMIXED-with-the-warning-of-Hessian-matrix/td-p/283766

Re: WARNING: The final Hessian matrix is full rank but has at least one negative eigenvalue

mkeintz — Sat, 10 Jul 2021 05:16:57 GMT

"Final Hessian"

Somebody should take that as a username.

Re: WARNING: The final Hessian matrix is full rank but has at least one negative eigenvalue

SteveDenham — Mon, 12 Jul 2021 12:51:57 GMT

If the Hessian is full rank with a negative eigenvalue, you have two options. One is to use a simpler model, the other is to find out which line of data (or lines) lead to the problem. You could use a pseudo-jackknife approach to the latter, fitting the model while successively deleting a single observation. If all of the reduced datasets lead to the same issue, then it is almost certainly a misspecification of the model issue.

SteveDenham