[R] Maximum likelihood estimation of parameters make no biological sense

[dave fournier]

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