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Thierry_S
Level VI

Help with Fit Model > Standard Least Square > Transform > Logistic

Hi JMP Community,

 

I'm struggling with the proper implementation of the Transform option in the Fit Model > Standard Least Square platform.

 

In order to better understand the issue, I created a mock data set where the Response is continuous; and the Model effects are: 1) Biomarker levels (continuous), 2) Treatment (2 categories), and 3) their interaction. The Response in the ACTIVE treatment is dependent on the Biomarker level following a logistic distribution

 

Here is a Graph Builder depiction of the response by biomarker levels:

Response x Biomarker Logistic.png 

If I run the Standard Least Square model with Treatment, Biomarker, and Interaction with the Response response transformed according to a Logistic relationship (Transform > Logistic on Response), I get an odd result:

 

1) Predicted by Actual (note the poor fit for most of the ACTIVE group [RED])


Response x Biomarker Logistic FIT MODEL LOGISTIC transformation.png

The residuals from this model are skewed as shown in the next 2 pictures:

2) Residuals plot

Model Fit Residual with Logistic Transformation.png

3) Residuals distribution

Distrib Resiudal with LOGISTIC Transformation.png

Clearly, I'm doing something wrong so please, help me figure out this apparently simple option.

 

Thank you for your help.

 

TS

Thierry R. Sornasse
4 REPLIES 4
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Re: Help with Fit Model > Standard Least Square > Transform > Logistic

Perhaps using the Analyze -> Specialized Modeling -> Fit Curve platform can help? You can fit a simple OLS model to the PBO group and a 4 - P logistic model to the treatment group.

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Thierry_S
Level VI

Re: Help with Fit Model > Standard Least Square > Transform > Logistic

Thanks for your suggestion: I can get a very nice fit to my mock data but I cannot figure out how to use this information in the Fit Model platform.

Any thought?
Thierry R. Sornasse
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dale_lehman
Level VI

Re: Help with Fit Model > Standard Least Square > Transform > Logistic

Having played around with some simulated examples, I am also a bit puzzled.  But I believe the problem you are having is due to the logistic transform in JMP.  According to the JMP documentation, the logistic transform is for the response variable to be in the range of (0,1).  Indeed, when I use that transform, I get something that does not look like a logistic function - when I hardwire the logistic function (which allows the response variable to take its correct values) it does look logistic.  So, I believe the logistic transform in JMP is not truly letting you fit a logistic function to your data.  Perhaps someone whose math is less rusty than mine, can explain how to use the logistic transform to get the correct shape when the response is not in the (0,1) range.

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Thierry_S
Level VI

Re: Help with Fit Model > Standard Least Square > Transform > Logistic

Thanks for your reply. Actually I scaled my response to be within the 0 to 1 range
((R-Min)/(Max - Min)) and the Logistic transform yields the following

Scaled response Logistic Transform.png.

If you look carefuly, the fit curves are not straight lines but still this is far from a tight fit.

 

Any thought?

Thierry R. Sornasse
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