Fit data to a logistic function with a known asymptote

[#1]

My goal is to fit this data to a logistic function (Logistic 3P for example). The y variable represents a proportion, so the maximum possible value is 100%. So I need to specify the asymptote as 100% because the model gives me values up this limit, and this is empirically impossible (attached image).

Thak you for the help. 

[#2]

It's hard to tell from just the screenshot: are you using Fit Curve, Nonlinear, or FDE platforms? Also, is it possible to share an anonymized set of the data to work with?

[#3 · Accepted solution]

If I understand correctly, you need to fit Logistic-2P, because the asymptote is known.

In that case, you need to normalize your data, such that Y is between 0 and 1. In your case, I guess that you should divided your Y by 100.

After that, the Logistic-2P will be available:

Scaling your data should not impact the other two parameter estimates, i.e. the remaining two estimates are same. Unless you want to do some kind of prediction of Y given "cp", then your need to scale back after prediction using the fitted model.

[#4]

Thank you so much! I have another doubt related to this kind of analysis. 

When I try to compare parameter estimates, I obtain this error: 

And when I try to make a custom inverse prediction, the std error in two variables is massive (the others are so good): 

Is it possible that these two treatments cannot be modelled? Is there a possible solution? They are the two curves marked with an arrow (yellow and purple).

Thak you for the help to all users!

[#5]

There is not enough information here so that I can tell what is going on. From the fitted curve, I suspect the Growth Rate estimates of those two are relatively large. From the inverse prediction, seems the models have large uncertainties. I cannot tell where the uncertainties are from based on what I see here.

[#6]

Thank you for you help Peng. 

If you want, I can pass to you an anonymous data set to "play" with it, to discover what is happening here :).

[#7]

Should you be concerned at the lack of parallelism among these curves?

[#8]

Hello Mark, 

Not so much, because they are different treatments, and each one reacts different. If you want, I can send you an anonymous dataset to investigate it :). 

Thank you so mucho for your help!