I'm fitting a three parameter sigmoidal function to acquisition data (i.e., learning, breaking points, curvature index) and I need to find a simple way to describe what is happening with my curves.
Dear Marina,
The parameters of three parameter sigmoid functions are usually labelled as the upper asymptote, slope (growth rate) and the crossover point (time of maximum growth) respectively. So I am not sure which equation you are referring to - but hopefully you can map this on to the equation you are using.
Best of luck
Thank you very much, Bruce!
The equation is m/(1+exp((-(t-c))/s))
c=center s=scale m=maximum rate
My concern is about how to manage the fact that the value of s parameter depends on the value of the c parameter...I have been reading a book about models to biological data with nonlinear regression but it was not pretty specific about this issue.
Marina,
Your main variable is learnig distributed on some time. If you have a sample of size N=20 cases and publish them here I may work and graph them to explain its braking points and curvature. You do not need to give details about units and methods used to measure learning. emilio
Dear Marina,
I would rather you said that the value of c is relative to that of s in this context. "s" or scale allows you to capture the distance between the floor and ceiling values, with "c" telling you at which point the slope actually occurs. While it is true that they jointly determine "slope" (a poorly consider word choice with a continuous logistic curve) they are dissociable. So for your discussion it would usually be acceptable to discuss changes in "c", and "m" as occurring separately so long as "s" was constant or similar between conditions. Similarly for the other combinations. If all three parameters differ then it is easiest to simply say that they have "different" shapes.
Hope this helps.
Thanks, Bruce.
Your explanation is very useful...that's exactly what I wanted to know!
y=m/(1+exp((-(t-c))/s))
m= max growth
s=growth rate
c=crossover, a point where the curve changes direction, we call it also infliction point
Thank you for your answer, El Yousfi Brahim. The point is that I'm fitting a sigmoidal function per group of animals. Animals were submitted to different treatments and I want to determine if there is a difference between growth rates, but I don't know if I need to have constant c values (which, usually, is not the case in my data). Reviewers had questioned the point. Any idea about how to capture these subtle but orderly changes in learning? My analysis level is session by session. THanks!!
C may also be looked at for your animals because at c level (wich is time usually) refers to where growth changes from fast to slow motion.
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