Re: Maximum likelihood estimation of parameters make no biological sense
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
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
# Number of parameters = 5 Objective function value = -11.6954 Maximum
t component = 0.00000
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
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.