Did some quick research, and what it comes down to is that nonlinear regression is a bitch. It can become extremely heavy computationally, slow, and bulky, not to mention inaccurate if outliers are factored in incorrectly. Several algorithms have been developed that will crank out some pretty nice results, but what it comes down to is that it is an inherently impossible task. As this guy named Dr. Harvey Motulsky (an expert on nonlinear curve fitting) says:
QUOTE
Some programs (not available from GraphPad Software) automatically fit data to hundreds or thousands of equations and then present you with the equation(s) that fit the data best. Using such a program is appealing because it frees you from the need to choose an equation. The problem is that the program has no understanding of the scientific context of your experiment. The equations that fit the data best are unlikely to correspond to scientifically meaningful models. You will not be able to interpret the best-fit values of the variables, and the results are unlikely to be useful for data analysis...Don't use a computer program as a way to avoid understanding your experimental system, or to avoid making scientific decisions.
Basically, we have to church through thousands of models and compare the results of each when applied to the dataset, and then choose the best one programatically. Some models can be pruned or ignored off the bat because of the nature of their patterns, but the vast majority will have to be computed.
In other words, I can't wait to break this bitch of a puzzle. It will be done if it's the last thing I do.
Edit: Progress already! The same dude has a nice web page set up devoted to the difference between curve-fitting and regression, and the pros/cons of each. Using curve-fitting it is not necessary to choose a model, so basically you skip the step of computing those 1000s of possible set ups. Although it is less accurate, a cubic spline or lowess curve should serve our purpose well enough. That said, it's still going to be a bitch to code the algorithm that computes the curves, as they tend to be nearly impossible to convert into a usable equation form, and the math is still way over my head I believe... I'm pretty excited now though