MATLAB: Fminsearch for fitting models

fittingfminsearchMATLAB

Good afternoon, I'm quite a newbie in MatLab, and I'm trying to use the fminsearch function to fit both a normal and a sigmoidal/logistic models to my data. At the moment, I'm using the following formula for the logistic: [par fit]=fminsearch(@(p) norm(1./(1+exp(-p(1).*(X-p(2)))) -Y), [1,1]);
X corrisponds to 10 different location of a stimulus, while Y is the answer (0/1) given to the stimulus. However, the outcomes I obtain in this way seem totally untrustworthy, even if the formula is the correct logistic formula. There is something I'm missing?
Thank you in advance, Alessandro

Best Answer

When in doubt, simulate:

p = [2 5];
X = 0:20;
Yfcn = @(p,X) 1./(1+exp(-p(1).*(X-p(2))));
Y = Yfcn(p,X) + 0.1*randn(size(X));
[par fit]=fminsearch(@(p) norm(1./(1+exp(-p(1).*(X-p(2)))) -Y), [1,1])

figure(1)
plot(X, Y, 'p')
hold on
plot(X, Yfcn(par,X), '-r')
hold off
grid

It looks good to me, and the parameter estimates are appropriate. If you are not getting reasonable results, experiment with different initial parameter estimates.

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