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Functional Data Explorer Target Curve

Good morning,

In the Functional Data Explorer, is it possible to define the desirability of a target curve? Because when I'm in the Functional Experiment Design Profiler, I can't define desirability across the entire curve, only at a point X.

Similarly, in the simulator, is it possible to build a data table with a certain number of experiments where JMP Pro calculates all the points of the curve and not just the X value defined in the Profiler?

Thank you in advance for your help.

Design of Experiments Re: Explorateur de données fonctionnelles Courbe cible

Hello @SquaresJackal10,

You can add a target curve/function in the data processing options of the Functional Data Explorer: Data Processing Options (Commands > Target Functions). This way, when clicking on "Show Target Profilers", it will add in the FPC prediction profiler two lines of profilers and the option to optimize the curve function to match closely the one entered as a target:

If you have used a Functional DoE analysis (and provided the model is reliable and accurate), you can save the Prediction formula in your table from the red triangle next to "Functional DoE Analysis". You can then create a new table with any X values and copy-paste the prediction formula in this table to predict curves.

Hope this answer will help you,

Re: Functional Data Explorer Target Curve

Thank you very much for your answer. It helped me a lot. However, how do I ensure the model is reliable and accurate in this module? Does it work like a standard experimental design, or are there some nuances?

Thank you again.

Re: Functional Data Explorer Target Curve

Hello @SquaresJackal10 ,

Given that the modeling will be carried out in several stages (first fitting the curves using a model, then reducing dimensionality through the identification of shape functions and the estimation of their coefficients, then modeling the coefficients of the functional model as a function of the factors), there are three points of attention to use the final model to optimize and predict curves:

1. Ensure that the curve modeling is sufficiently accurate and that the fitting does not introduce any particular bias. To do this, the diagnostic plots in the report allow you to assess how well the model fits the data. An example is shown here using the JMP NMR DOE dataset:
   
   

2. Next, evaluate the appropriate number of principal functional components to achieve sufficient accuracy in predictions while maintaining an adequate number of shape functions and associated coefficients (to avoid an overly complex model that risks overfitting). Here is an example using the same dataset as before (the number of shape functions and coefficients to determine is relatively high because the functional data used here are NMR spectra, so fitting the different peaks and regions requires a fairly large number of shape functions (and associated coefficients) to avoid losing information about the spectra):

   
   

3. Finally, verify the default model generated by JMP when performing a DoE functional data analysis. The goal of this step is to model the coefficients of the shape functions found in the previous step using the factors from the experimental design (or more generally, the factors/predictors/features from the data table). This part is often overlooked by users, but it can lead to incorrect interpretations or predictions if not handled properly.
   We can examine the diagnostic plots, and in case of patterns or significant inaccuracies/defects in the model, we can check each generalized regression model for each coefficient to improve the modeling of that coefficient. However, we will lose precision at each step because we are increasingly "summarizing" the information: first, we take a functional model that approximates the curves, then we reduce the dimensionality through functional PCA, and finally, we try to model the coefficients of the conserved principal functions.
   The most important thing is to have the first coefficients correctly modeled, because they are the ones that will concentrate most of the information from the curves by modulating the impact of the associated shape functions (see previous FPCs eigenvalue graph).

   
   

Hopefully this answer will help you.

Re: Functional Data Explorer Target Curve

Thank you very much, that's much clearer to me.

However, for "steps 1 and 2", I have no residues. I've never obtained this before, is that normal?

Diagnostic Wavelets and Graphs

Functional PCA:

 

However, I do have some differences between the Y values ​​obtained and those predicted in the functional DOE analysis:

THANKS

Re: Functional Data Explorer Target Curve

Wavelet models are quite accurate and flexible, so it's not surprising to have zero residuals. You can try other functional approaches besides wavelets (notably P-splines, or B-splines if your curves have easily identifiable patterns like quadratic/cubic/etc.) to see if you get the same result. If so, it simply means that your curves are very well modeled by this type(s) of model(s).

On wavelet models, functional PCA recommends a high number of components, so there is little "information compression", so again it is not surprising to find ourselves in a situation similar to the previous one with zero residuals.

The final diagnosis shows that your complete model has correctly captured the trend in your data and that there do not appear to be any biases or patterns in the residuals, including random variation of the residuals around 0 and homoscedasticity of the residuals .