Bruce McCullough wrote:
> > While trying to fit a nonlinear model using nls( ), I get an error
message
> > that says I have a singular gradient matrix. I am not sure what causes
> > this problem. Should I try different initial values of the parameters,
or
> > is the problem something else?
>
> I have found that supplying analytic first derivatives
> using deriv() can eliminate this problem (not always,
> but sometimes). Supplying analytic derivatives
> is well-described in V&R.
>
>
I'll add a few lines of my partial ignorance. In addition to the advise
thatBill Venables and Doug Bates (and others?) have given, there is another
approach.
The optimization can be done by a more robust method such as a genetic
algorithm. This is "robust" in the computational sense, not the statistical
sense. A genetic algorithm can handle non-differentiability, and multiple
local minima. There is a crude implementation of a genetic algorithm in
S that is given in S Poetry. In this setting, the use of the genetic
algorithm would be to give a very good starting value to a more traditional
optimizer.
However, it is my experience that it is often the case that severe problems
with convergence means that the data don't fit the model very well. It
may be worth having a think about the suitability of the model from time
to time when convergence is a problem.
Pat
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