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.)

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

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.