Fitting sigmoid to data

Question

There are many curve fitting and interpolation tools like polyfit (or even this nice logfit toolbox I found here), but I can't seem to find anything that will fit a sigmoid function to my x-y data.

Does such a tool exist or do I need to make my own?

Answer 1

nlinfit, and especially gatool, are big hammers for this problem. A sigmoid is not a specific function. Most commonly it is taken to be the same as the logistic function (also often the most efficient to calculate):

y = 1./(1+exp(-x));

or a generalized logistic. But all manner of curves can have sigmoidal shapes. If you know if your data corresponds to one in particular, fitting can be improved and more efficient methods can be applied. For example, the error function (erf) has a sigmoidal shape and shows up in the CDF of the normal distribution. If you know that your data is the result of a Gaussian process (i.e., the data is the CDF) and you have the Stats toolbox, you can use the normfit function. This function is based on maximum likelihood estimation (MLE). If you end up needing to write a custom fitting function - say, for performance reasons - I'd investigate MLE techniques for the particular form of sigmoid that you'd like to fit.