Hi,
Your results are do to using an unstable parameterization
of the Von Bertalanffy growth curve, combined with the unreliable
optimization methods supplied with R. I coded up your model in
AD Model Builder which supplies exact derivatives through
AD.
I used your starting values and ran the model with no optimization steps
just to se that we had the same value for the -log-likelihood
Results are
# Number of parameters = 5 Objective function value = -11.6954 Maximum
gradien
t component = 0.00000
# winf:
24.2720681300
# k:
0.0467984400000
# t0:
0.00100000000000
# vhat:
0.0100000000000
# b:
1.61760492000
However the R routine is stuck. When I let the ADMB code run it produced
# Number of parameters = 5 Objective function value = -13.8515 Maximum
gradient component = 9.41643e-05
# winf:
15.7188821203
# k:
0.118198731245
# t0:
-32.9089295327
# vhat:
0.00471832483493
# b:
184.999879271
Note that b--> infinity. I have it bounded at 185.
t0--> -infinity so that the model is only using a small part of the
growth curve which happens to fit the data better.
The estimated correlation matrix for the parameter estimates tells the story
index name value std dev 1 2 3 4 5
1 winf 1.5719e+01 5.1252e+00 1.0000
2 k 1.1820e-01 2.7849e-02 -0.9832 1.0000
3 t0 -3.2909e+01 7.6867e+00 -0.9748 0.9990 1.0000
4 vhat 4.7183e-03 2.0119e-03 0.0000 0.0000 0.0000 1.0000
5 b 1.8500e+02 1.6374e+00 -0.0002 0.0003 -0.0094 0.0000 1.0000
You can see that several of the parameters are highly confounded.
Also the eigenvalues of the Hessian are
0.01691149331 0.02045399106 963.2994413 2255.900979 4225373.963
So you have a condition number of about 10^8. Very difficult to work
with such a function with only approximate derivatives.
I think the moral of the story is that you should use a more stable
parameterization or an industrial strength estimation system or maybe
both.
Cheers,
Dave
Cheers,
Dave
--
David A. Fournier
P.O. Box 2040,
Sidney, B.C. V8l 3S3
Canada
Phone/FAX 250-655-3364
http://otter-rsch.com
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