COMPGROUPS.NET | Search | Post Question | Groups | Stream | About | Register

### SAS - proc nlmixed & Cholesky Decomposition

• Email
• Follow

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

In order to deal with the following problem:
WARNING: The final Hessian matrix is full rank but has at least one
negative eigenvalue.
Second-order optimality condition violated.

I have used the Cholesky parametization as suggested by numerous
sources (book, etc)
The code is the following:
------------------------------------------------------------------------------------------------------------------------------------------
proc nlmixed data=patient method=firo;
parms Min=95 Max=105 EC50=1000 Slope1=-0.5 Slope2=-0.5 s2e=0.5 t11=0
t22=0 t33=0 t44=0 t12=0 t13=0 t14=0 t23=0 t24=0 t34=0;

part1 = (Max) - (Min+u2);
part2 = 1+ (1/(1+((time/(EC50+u3))**(2*(Slope1+u4)*(Slope2+u5)/
(ABS((Slope1+u4)+(Slope2+u5)))))))*((time/(EC50+u3))**(-(Slope1+u4)));
part3 = (1- (1/(1+((time/(EC50+u3))**(2*(Slope1+u4)*(Slope2+u5)/
(ABS((Slope1+u4)+(Slope2+u5))))))))*((time/(EC50+u3))**(-
(Slope2+u5)));

cov1= t11*t11;
cov2= t11*t12;
cov3= t11*t13;
cov4= t11*t14;
cov5= t12*t12 + t22*t22;;
cov6= t12*t13 + t22*t23;
cov7= t12*t14 + t22*t24;
cov8= t13*t13 + t23*t23 + t33*t33;
cov9= t13*t14 + t23*t24 + t33*t34;
cov10= t14*t14 + t24*t24 + t34*t34 + t44*t44;;

model vol ~ normal((Min+u2)+(part1/(part2+part3)), s2e);
random u2 u3 u4 u5 ~ normal([0,0,0,0],
[cov1,cov2,cov3,cov4,cov5,cov6,cov7,cov8,cov9,cov10]) subject=patient;
run;
---------------------------------------------------------------------------------------------------------------------

Assuming I have done things correctly, I no longer get the negative
eigenvalue in Hessian Matrix message.
& I do get stats (estimates, p-values, etc) for the t11, t12,
t13, ...t44 & so on.

My question is, how to apply the stats to the var-covar matrix
elements.
for the estimates, should I use the formula that I have defined above?
i.e. the estimate for covariance element 3 would be the multiplication
of the estimates for the t11 & t13: cov3 = t11*t13 ?

Would it be the same for the p-values?
should the p-value for the covariance element 3 be the multiplication
of the p-values of t11 & t13, for example?
But the problem is that if I use this method, I get some p-values that
are over 1. That's what makes me confusing.

Any help would be appreciated.

Thank you very much
```
 0

See related articles to this posting

0 Replies
716 Views

Similar Articles

12/1/2013 10:30:24 AM
page loaded in 93746 ms. (0)