Problem with 'second order optimality condition' in proc nlmixed

[issac]

Hi everyone;

Am working with 9.3 version. I submit the following code :

proc nlmixed data=x;

lambda=exp(b0+blogdisage*logdisage+bloglos*loglos+bpows*powsYES

    ++b1mar*marMARRIED+b2mar*marPREVIOUSLY_MARRIED

    +bseq*seq+e);

ll=-lambda*rtime**(alpha+1)+rstatus*(LOG(alpha+1)+alpha*LOG(rtime)+LOG(lambda));

MODEL rtime~GENERAL(ll);

RANDOM e~NORMAL(0,s2) SUBJECT=id;

PARMS b0=1 blogdisage=0 bloglos=0 bpows=0 b1mar=0 b2mar=0 bseq=0 s2=1 alpha=0;

run;

and got this notice in log:

NOTE: FCONV convergence criterion satisfied.

NOTE: At least one element of the (projected) gradient is greater than 1e-3.

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

         Second-order optimality condition violated.

I could not understand what's happened but I have got the following parameter estimates that has nothing for S2 (Random Variance).

b0	0.7987	0.6933	2443	1.15	0.2494	0.05	-0.5608	2.1582	717.9996
blogdisage	-0.7512	0.1124	2443	-6.68	<.0001	0.05	-0.9717	-0.5308	2882.034
bloglos	-0.1244	0.03542	2443	-3.51	0.0005	0.05	-0.1939	-0.05496	834.6029
bpows	0.2024	0.4954	2443	0.41	0.6829	0.05	-0.7691	1.1740	-717.951
b1mar	0.03810	0.04843	2443	0.79	0.4315	0.05	-0.05687	0.1331	34.79886
b2mar	0.06841	0.04097	2443	1.67	0.0951	0.05	-0.01194	0.1488	190.9215
bseq	-0.1507	0.03239	2443	-4.65	<.0001	0.05	-0.2142	-0.08721	829.1515
s2	-111E-14	.	2443	.	.	0.05	.	.	234.112
alpha	-0.4764	0.02492	2443	-19.12	<.0001	0.05	-0.5252	-0.4275	2446.752

Appreciate your comments on this.

Thanks!

Issac

[SteveDenham]

This is all a guess, without seeing the data structure.  I think there is a "complete solution" to the existing data, given the fixed effects, leaving no variability from individual to individual after accounting for all fixed effects.  I certainly would not trust any of the standard errors or tests, given that the Hessian is non-positive definite.  It may be that the model is over-specified.  What happens if you drop some of the fixed effects?

Steve Denham

[issac]

Steve;

Thanks for your response. When I drop 'e' (random effect) from the model new error named "Floating Point Zero Divide" has shown up. Also when I exclude some of categorical columns, it did'n change anything. I also check the over specification condition and almost sure that it is not the case in the model. 

[lvm · Accepted solution]

Check out this excellent article from the most recent SAS Global Forum.

http://support.sas.com/resources/papers/proceedings12/332-2012.pdf

This paper deals with most of the common errors and warnings one can receive using the mixed-model procedures. Your Warning is discussed on page 14 (with good corrective hints).

[issac]

Ivm;

Thanks so much for bring this good paper into my attention. That's great!

Issac