A Tip for FDE Demo

jiancao

A focus of FDE in JMP Pro 14 is perform functional PCA and then use the fPCs as inputs into a predictive model. The example in the JMP Documentation shows the use of GenReg to identify significant fPCs.  https://www.jmp.com/support/help/14/additional-example-of-the-functional-data-explor.shtml#240860.

To directly demonstrate the benefit of using fPCs in predictive modeling, let’s fit two standard least squares models: one with fPCs (left) and the other with the average measurments for each process variable (right). The difference in RSquare adj. is striking: 0.78 vs 0.12! The traditional approach of averaging throws away information that explains the variability in yield.  

Data with saved script is attached.  FDE models that I ran are B-splines of degree 3 on initial data.

Fermentation Process Yield with fPCAs.jmp

JerryFish

This is great Jian, Thank You!

 

So I'm thinking that a good way to present might be:

1. "Here is some functional data.  Currently, how might you handle using the data to predict Yield?"  (Answer almost certain to include "Use Average")
2. Model using average, show how poor the predictive ability is
3. "What if we could take into account the functional characteristics themselves?"
4. Introduce FDE.

Still need some additional tools like:

1. Once you have the optimum fPC values for maximizing yield, what do the optimum individual functions look like?
2. A profiler-like function would be nice to handle "What If" questions.  Input either fPC values or possibly drag around functional shapes (via spline adjustments) and predict yield??

Thanks again Jian!  I'll use this next week!