Multivariate analysis for non-normal distribution (not transformable)?

[#1]

Dear JMP community,

I need to analyze the effects of treatment and multiple biomarkers on an clinical outcome variable that is not distributed normally (see histogram below).

Based on my limited knowledge, I'm pretty sure that I cannot use the Standard Least Square model for the analysis of this data since the error generated by the model is not distributed normally. So, what would be my best option to achieve my goal?

Note: I'm using the standard version of JMP 11.1

Thank you for your help.

Sincerely,

[#2]

I think it is hard to respond generally to your question (at least it's hard for me) without more context.  But looking at this distribution of your clinical outcome makes me think you might want to consider this as a discrete outcome.  The distribution is strongly bimodal - might it be possible to group all values < .5 into the 0 bin and >.5 into the 1 bin and then analyze it as a classificaiton problem?  Of course, if your sample size is large enough, linear models might provide a reasonable estimate for the mean - but with a bimodal outcome like this, the mean is not particularly of interest.

[#3]

Hi Dale,

Thank you for your suggestion: I had already experimented with the bining the clinical outcome variable into 3 levels which seems to perform well with the Ordinal Logistic model.

Best,

[#4 · Accepted solution]

Something you can try is Neural Nets under the Analyze Menu.  Neural Nets are a good platform for trying to fit non-linear data.  I am not sure if it is a standalone platform in JMP 11 or if you will find it under Predictive Modeling.  You can try several levels of the TanH function to see if you get a good fit.  One thing to remember is that NN models are easily overfit if you don't use some sort of cross-validation.  Use K-fold or Holdback and try different levels.  If you have a small data set use Leave-One-Out validation.  If you don't see that listed you can use K-Fold and make the number of rows your Number of Folds.

HTH 

[#5 · Accepted solution]

Have you thought about using the Partition Platform? You've certainly got splits in your response variable distribution just screaming at you. Biomarker predictor variable data is also often notoriously full of multi collinearity...so a technique such as PLS might show some insight?

[#6]

Hi Peter,

Thanks for suggesting the Partition Platform. Is there a way to capture the significance of the parameters used to split the response?

Thank you for your help.

Sincerely,

[#7]

@sornasst:

I would definitely look at the basic response plot, Column Contributions, and Log Worth values that populate many of the different analysis platform report windows. And I also heartily endorse using all the cross validation techniques that my colleague @Bill_Worley mentions as well. You can just as easily overfit a regression tree as you can other modeling methods. Here's a link to the general online JMP documentation for the Partition Platform. Since you are using JMP 11, this documentation is for version 13...so some of the options or menus may be different or nonexistent...but it can at least get you started.

http://www.jmp.com/support/help/13-2/Partition_Models.shtml#

[#8]

...and, in addition to the modeling methods mentioned above, I want to call your attention to the Assess Variable Importance (a.k.a. the Sobol'izer)  pulldown in the Prediction Profiler.

Neural nets, in particular, are notorious for being "black boxes" that don't provide information about variable importance, and the Sobol'izer remedies that issue pretty righteously.  A reference is attached.