How can I improve the mixed model when I encounter non-positive hessian or non-positive definite G

[Ethan_Kael]

When I solve the semi-repeated crossover design data according to the procedures of FDA equivalence guidelines, I find that sometimes the hessian is not positive definite or G is not positive definite. In most cases, the hessian is not positive definite quite frequently. I know it could be because the dataset is not enough, the model is too complex, such as multicollinearity, or lack of information in certain directions of the parameter space.Based on some advice on the Internet and mixed of sas documents, I would use parms statements such as:

parms 0.1,0.1,0.1,0.1,0.1/ lowerb=1e-10,.,1e-10;

Sometimes we need to adjust the initial values, otherwise the hessian will still be non-positive.

I would like to ask whether the model needs to adjust or ignore the information when the hessian is non-positive definite. In general, how to adjust to eliminate this note, do I need to adjust the initial iteration value over and over again?

The following is my program, I hope to get some suggestions:

proc mixed data=pk;
class sequence subject period formulation;
model lncmax= sequence period formulation/ ddfm=satterth singular=1e-10;
random formulation/type=FA0(2) SUB=subject G ;
repeated/ grp=formulation sub=subject ;
parms 0.1,0.1,0.1,0.1,0.1/ lowerb=1e-10,.,1e-10;
estimate 'T vs. R' formulation -1 1/cl alpha=0.1;
lsmeans formulation / pdiff=control("R") alpha=0.1 cl;
run;

[Ksharp]

https://blogs.sas.com/content/iml/2019/04/03/g-matrix-is-not-positive-definite.html

[Ethan_Kael]

Thank you for your answer. Of course, I have read this article before. There is no parms statement in the initial program, I use ods output ConvergenceStatus=ConvergeStatus to get the value of pdh to decide whether to use parms statement, when G matrix appears, According to this article, I hope to get satisfactory results by removing random statement or changing type=, such as type=FA0(1).

However, most of the time, the hessian is not positive definite, and I set some initial values with parms statement, but it still does not change, so I want to know how to change the code, or how to change the initial value with theoretical basis instead of constantly changing the initial value to see if the result is positive definite

[PaigeMiller]

Do an internet search for "Hessian non-positive definite", plenty of advice out there.

[jiltao]

For the Hessian not positive definite message -- you might try rescaling your data values, or simplifying your model. 

For the non-positive definite G matrix -- you might try simplifying the random effects.

It is always a good idea to examine the output, which might give you ideas on the next steps of dealing with this type of issues.

Jill