Take a quick look at the answer here:

http://mathematica.stackexchange.com/questions/21823/methods-for-nonlinearmodelfit

So basically, you can use methods from FindMinimum and NMinimize. I'm not sure how well the NMinimize examples work.

What i find is that NonlinearModelFit behaves like a blind dog in a butcher shop.

Yes. That's the nature of minimization and root finding.

Thanks to both of you for your responses. I have been studying the material from the various links, much of which I have read before. I could still use more study. The problem at hand is very sensitive to the start point, so I have been looking for methods which would seek a local optimum, rather than get distracted by a global search.

I am finding it difficult to discover what methods are available to NonlinearModelFit. Many I try, including methods from FindMinimum and NMinimize return either as not available. Returning:

"Value of option Method -> \!(\"FindMinimum\") is not Automatic, \ \"Gradient\", \"ConjugateGradient\", \"InteriorPoint\", \"QuasiNewton\ \", \"Newton\", \"NMinimize\", or \"LevenbergMarquardt\""

Or not available for constrained problems:

NonlinearModelFit::ucmtd: Method -> Gradient can only be used for unconstrained problems. >>

In fact, the only method I find accepted (other than automatic) is Interior Point.

I will of course continue to study, but if anyone knows of documenation on methods specific to either NonlinearModelFit or FindFit I would be grateful.

Thanks and kind regards,

David

Thanks, Frank. That is what I had come to suspect. The constraints arise from two sources. The important one is physical. Many of the parameters are probabilities, which must be 0<=p<=1. Others are initial values of counts, which cannot be negative. I am concerned that a fit could be found that violates these. I added some constraints to try to help the fit by boxing in some parameters to reasonable values. I will see how things go with no constraints -- my fears may be groundless. I had also been thinking to roll my own fit with FindMinimum -- it sounds like a good idea.

The workings are a bit frustrating, in that with a five-parameter manipulate I can quickly close in on a good-to-the-eye fit myself. However, it is probably unfair to judge the Mathematica algorithms by that standard. In thinking about what I am doing, I very quickly recognize that some parameters control the form of the curve, and others its placement in y and slope. So I manipulate the two sets alternately to home in on the fit. (Perhaps someone has tried similar things algorithmically, by fitting the 1st derivative, second derivative and the values iteratively.)