Hi Dave,
first of all, fitting starting values of a dynamic model the same way
like its parameters is indeed the usual method. In that case parameters
*and* some or all initial value(s) of the dynamic model are both in fact
'parameters' for the statistical model fitting problem.
Fitting a nonlinear model can be easy or problematic or even impossible,
depending on the data and the model structure. In such cases one speaks
about "identifiability" and there are several methods that can help to
find parameter combinations that can be identified simultaneously.
It is not important whether such a statistical parameter was
originally a 'parameter' or an 'initial value' of the dynamic model,
it simply depends on collinearity of the problem:
http://en.wikipedia.org/wiki/Multicollinearity
Several methods for identifiability analysis are provided in the CRAN
package "FME" (Flexible Modelling Environment), which comes with
extensive documentation (package vignettes as pdf files) and examples
and there is a recent paper in the Journal of Statistical Software:
http://www.jstatsoft.org/v33/i03
Look for function 'collin' that implements a collinearity index.
In addition, function 'modFit', that is also in this package provides an
interface to use different optimizers of R in a unique way, namely nls,
nlminb, optim, nls.lm (from package minpack), and pseudoOptim, a
pseudo-random search algorithm.
Another hint, because you are still using "odesolve" (from Woodrow
Setzer). This package has now a direct and compatible successor
"deSolve" (Soetaert, Petzoldt, Setzer), see:
http://www.jstatsoft.org/v33/i09
deSolve is even more stable than the former version and contains many
many more solvers, not only lsoda and rk4, can handle other types of
differential equations too and has much more documentation.
Hope it helps!
Thomas Petzoldt
PS: There is also a dedicated mailing list for such questions:
https://stat.ethz.ch/mailman/listinfo/r-sig-dynamic-models
--
Thomas Petzoldt
Technische Universitaet Dresden
Institut fuer Hydrobiologie
01062 Dresden
GERMANY
http://tu-dresden.de/Members/thomas.petzoldt
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