Fitting sigmoid data then determining value of x when y = 50%

Hi there,

Psychology PhD student who is attempting data analysis on MATLAB for the first time.

If I explain what I need to do:

(i): I need to fit a sigmoid curve to my data, via the curve fitting tool, if possible

(ii): I then want to find the value for x when y is 50%

Now, I've attempted to fit a sigmoid curve via the curve fitting tool by inputting the formula for it. It has given me some sort of y = mx + c (screen shot attached). Where have I gone wrong and, how do I acheive what I am trying to do?

Best wishes,

Matthew A

Answer 1

[Cris LaPierre]

Sigmoid models typically return a probability, and the 50% response corresponds to x=0. Therefore, you need to modify your equation a little. I elected to use the logistic function found here.

(1./(1+a*exp(-b*(x-450))))*100

Here, I've estimated that the X value of the 50% response is 450. Since the equation is designed to return a value between 0 and 1, I've multiplied it by 100 to make it go from 0-100.

In this case, I would likely incorporate the 50% point into the model and have it be a result of the fit.

(1./(1+a*exp(-b*(x-x50))))*100

However, this doesn't 'just work' as is. I had to modify the fit options to get it to give a decent result. This means you would have to know something about the expected values. Here's how I modified it.

To reduce the number of parameters estimated from the data, I set c=1.

[Matthew Hopkins]

Thank you very much.

And I take it that 0.48 is the value of x?

[Cris LaPierre]

No. That is the initial guess, but not the final value. For final values, look in the white box on the left labeled "Results". There it shows the final value of x50 was found to be 453.1.

[Matthew Hopkins]

Hi there,

Thank you. That makes sense.

Finally (sorry for all these questions!)

I have about 60 different subjects. When I want to fit this sigmoid function to each one's data points, I presume I simply adjust the graph by specifying in the 'lower' cell the point where the graph starts to rise, and in the higher, where it tapers off?

Best wishes,

Matthew A

[Cris LaPierre]

Ideally, you can find a range that works for everyone. I started with 200-600, but it didn't fit the curve until I increased the lower limit to 300 for the subject you show. The biggest problem is that there are so few data points.

You might have more success using fminsearch, where you can define your own cost function. My suggestion would be to research what techniques others in your field have used in their publications. You will likely find fit equations and cost functions that, at the least, are generally accepted and understood by the community.

[Matthew Hopkins]

Hi there,

Thanks for that. The main methods they describe is either fitting a regression line and calculating that, or using the sigmodial function

Best wishes,

MAtthew A