How do I solve WARNING:The final Hessian matrix is full rank but has at least one negative eigenvalu

ChantelleM — Tue, 07 Sep 2021 14:05:02 GMT

Hi!

I am trying to run a marginalised two part model with generalised gamma distribution for semicontinuous data to get the mean costs of all in my study population, rather than a mean conditioned on having expenditure. However after running the syntax below, I get the following warning in the log:

NOTE: Convergence criterion (GCONV=1E-8) satisfied.
NOTE: At least one element of the gradient is greater than 1e-3.
NOTE: Moore-Penrose inverse is used in covariance matrix.
WARNING: The final Hessian matrix is full rank but has at least one negative eigenvalue.
Second-order optimality condition violated

I have rescaled the cost outcomes from swedish krona to euros and this helped with some cost outcomes but not all. Any other suggestions/ solutions?

%macro mtpmacroms (a0 ,a1, b0, b1, kappa, x1, y);
proc nlmixed data=studypop1 MAXIT=1000 ;
/* provide starting values for parameters */
parms a0=&a0. a1=&a1.
b0=&b0. b1=&b1. kappa=&kappa.
s0=0 s1=0;
/* Specify mean model for binary part */
linbin=a0+(&x1.*a1);
binprob=exp(linbin)/(1+exp(linbin));/* prob y>0 */
eta=abs(kappa)**(-2);
/* Define heterogeneous variance as a function of MOVE status */
logsigma = S0+S1*&x1.;
sigma=exp(logsigma);
/* Add covariates to mean model, changing only first line */
mu=b0+(b1*&x1.)
- log(binprob) - (sigma*log((kappa)**2))/kappa
-log(GAMMA(1/((kappa)**2)+sigma/kappa))+log(GAMMA(1/((kappa)**2)));
/* set up likelihood */
if &y. =0 then loglik=log(1-binprob);
else if &y.>0 then do;
u=SIGN(kappa)*(log(&y.)-mu)/sigma;
loglik=log(binprob)+eta*log(eta)-log(sigma)-log(&y.)
-log(GAMMA(eta))-.5*log(eta)+u*sqrt(eta)-eta*exp(abs(kappa)*u);
end;
model &y.~general(loglik);
/* Function to predict mean total cost for everyone in dataset */
pred_&y.=exp(b0+b1*&x1.);
predict pred_&y. out=mtpgg_&y.;
/* Estimate functions of parameters */
estimate "multiplicative effect of &x1. on &y." exp(b1);
estimate "total &y. for PwMS" exp(b0+b1);
estimate "total &y. for references" exp(b0);
run;
/* get predicted mean estimates*/
proc sort data=mtpgg_&y.;
by MS; run;
proc means data=mtpgg_&y.;
var Pred;
by MS;
run;
%mend mtpmacroms;

%mtpmacroms (a0=-2.6864 ,a1=1.1718 , b0=9.1899, b1=-1.2885, kappa= 0.6116, x1=MS, y=hc_costs_eur);

starting values from a logistic model for a and glm (gamma log link) for b

Re: How do I solve WARNING:The final Hessian matrix is full rank but has at least one negative eigen

PaigeMiller — Tue, 07 Sep 2021 14:07:27 GMT

This has been discussed many times in this forum; please do a search for similar problems and answers.

Re: How do I solve WARNING:The final Hessian matrix is full rank but has at least one negative eigen

StatDave — Tue, 07 Sep 2021 14:31:27 GMT

From your description of your data, it sounds like your response is continuous and positive but also contains a mass of values (possibly many) that are zero. If that is the case, you might consider alternative methods that are described and illustrated in this note.

topic How do I solve WARNING:The final Hessian matrix is full rank but has at least one negative eigenvalu in Statistical Procedures

How do I solve WARNING:The final Hessian matrix is full rank but has at least one negative eigenvalu

Re: How do I solve WARNING:The final Hessian matrix is full rank but has at least one negative eigen

Re: How do I solve WARNING:The final Hessian matrix is full rank but has at least one negative eigen