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A Tip for FDE Demo

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.

Re: A Tip for FDE Demo

I really like this example Jian. But it might also be helpful to show the power of Generalized Regression when using the Validation column (note these results are from 14.1 and use a different subset of FPCs, so your results will be different in 14.0).

 

When using standard least squares in genreg, the Validation RSquare is low:

 

When using the Adaptive Lasso, it is much improved:

 

 

Re: A Tip for FDE Demo

These are really nice tools, Ryan, and great that they are coming in V14.1.  Thanks for the update!

 

(And the Functional Data Analysis (Ramsay & Silverman) arrived a few days ago.  Enjoying wading through the details!)

 

Re: A Tip for FDE Demo

Jerry, some of these other tools you mentioned are coming in 14.1 when you Save Summaries:

 

 

The Prediction formula uses FPC scores the reconstruct the function using the Mean and Eigenfunction formulas:

 

 

If you have a functional response DOE, you can also build models to predict FPC scores from the inputs (in this case AOS, AO, and XP 80) to reconstruct the functions using those input values:

 

 

Re: A Tip for FDE Demo

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!