Modelling logistic data with GLMM and non linear platform

[#1]

Hello,

I am trying to model the data for each treatment separately, for x and y to predict the value corresponding to x of y/100 = 0,5 and the inflection point of the generated logistic curve. I want a logistic model with 2P because assyp. is known (1). 

To do this, on the recommendation of a staff member (thank you very much) I am trying two different ways: using GLMM in Fit Model and the non-linear platform.

Starting with the problem I am having in GLMM, I have several questions about it:

1. How can I know the inflection point of that curve? I didn't find a menu option to show it. 
2. The error std. Using the binomial distribution (I have searched about it, and for proportions I think it is the best choice, but I am not sure) the error is so high in treatment C (one of the initial problems), but also in treatment A (I did not have this problem before). Is the distribution I have chosen the main problem?
3. Finally, using the binomial distribution, in many treatments the probability Chisqr is not significant for the “model”, but the goodness-of-fit statistics have a good value (I found it in a JMP answer in a community post). With this value of Chisqr, does the model have a good result?

Regarding the way of modeling with the non-linear platform, as you can see in the scripts, I have tried equations with different parametrization (and Log2P from JMP) but I have a problem when I press 'Go'. The result doesn't fit the curve I want, and I think it may be caused by the initial values of the parameters. Is there any form to estimate this initial value to avoid this error? Also, when I try to make a custom inverse prediction it fails. 

I attach in this post an anonymous dataset of the values. The objective is to obtain good result for that what I have tried in the scripts, despite of the data limitations. 

Thank you in advance. 

[#2 · Accepted solution]

Hi Kaik,

Thanks for your questions. 

1. For a Binomial regression curve, the inflection point is the point at a 0.5 probability (which you already found using the Inverse Prediction function).
2. I don't think the distribution you've chosen is the issue, rather it might be the sparsity of your data. You may get better results if you check the "Firth Bias-Adjusted Estimates" box in the Fit Model window. Here's a post by @Mark_Bailey that gives some background.
3. I'm not understanding the question. Perhaps someone else on the community has insight, or perhaps you could rephrase?

Regarding the non-linear question, you might have better luck with the Fit Curve platform, where you can see inflection points, do equivalence tests, compare parallelism, etc. I've attached a Fit Curve script to your original data table.

[#3]

Hello Jed, 

Thak you for your answer! I will try with the second point that you have proposed to me. The third point it's about the parameters that JMP provide us to say if the curve is adjusted or not, and how to interpretate it. 

[#4]

Hi @Kaik 

If you want to find the inflection point of the curve you can take the first derivative.

Getting first order derivatives 

See help documentation for additional details:  Help-->Search JMP

• additional numeric functions
• Model fit options save first derivative
  SeJMP save first derivative

[#5]

Hi @stan_koprowski : Setting 2nd derivative (wrt x)  = 0, then solving for x will get you the inflection point...