Fminsearch for fitting models?

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

Answer 1

[Star Strider]

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.

Answer 2

[Alessandro Zanini]

Thank you so much! The simulation runs perfectly, so I think I have problems with the X: probably only 10 positions are insufficient for the sigmoid

[Star Strider]

As always, my pleasure!

You have only 2 parameters, so 10 data points should be enough to provide good parameter estimates. The fminsearch algorithm is derivative-free, although it still requires initial parameter estimates that are reasonably close to the optimal estimates. I would continue to vary the initial estimates across a wide range of values to see if you can get a good fit. The initial estimate for ‘p(1)’ can be any positive value. An appropriate initial estimate for ‘p(2)’ would be mean(X).

Answer 3

[Alessandro Zanini]

Correct. Modifying the parameters the curve fits without problems, even in 10 positions. Thanks!

[Star Strider]

As always, my pleasure!

Answer 4

[Jeff Miller]

Alessandro, it sounds like you are fitting probit models and/or psychometric functions. If so, you might find some very useful routines here: Cupid . DemoProbit.m shows some examples of how you could fit such models with various underlying distributions (normal, logistic, etc).

[Alessandro Zanini]

Thanks! But the link leads to a "not existing" page

[Jeff Miller]

Sorry, here is the link in plain text: https://github.com/milleratotago/Cupid

[Alessandro Zanini]

Thanks again!