[R] question about model formula

Setzer.Woodrow@epamail.epa.gov Setzer.Woodrow at epamail.epa.gov
Thu Mar 6 20:45:14 CET 2003

I did not know about stepsize being an issue.  I had thought that
problems with convergence in this case were due to bad approximations of
the finite difference gradient.  I guessed that around the optimum,
numerical errors would come to dominate the gradient calculations,
causing convergence to fail.

I've found that the issue about confusing optimizers that use gradients
can sometimes be fixed by augmenting the original system of odes with
what I believe engineers call the sensitivity equations.  If your
original equation is
dg/dt = f(t, b), where b is a parameter to be estimated,
then include

d^2g/dtdb (be sure to remember the chain rule when doing this!)

with the original equation.  With some regularity assumptions, this
integrates to dg/db, which can be used to give nls a gradient to work

R. Woodrow Setzer, Jr.                        Phone: (919) 541-0128
Experimental Toxicology Division             Fax:  (919) 541-4284
Pharmacokinetics Branch
NHEERL B143-05; US EPA; RTP, NC 27711

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