Model a functional response using a functional factor

[#1]

Hi,

Is it possible to model a functional response based on a functional factor?

I'm familiar with the Functional DOE Analysis option when I fit a model to a functional response but I've only found it possible to add non-functional / single-column factors. 

Any ideas would be much appreciated.

Kind regards,

Alicia

[#2]

You can save the functional PCAs for both the response and factor curves. Then, you can use them in the Y and X roles, respectively.

[#3 · Accepted solution]

Hi @Alicia Alicia,

It's definitely possible but can be an undertaking to be able to correctly interpret the results. You would need to do the following:

Set up a functional input model:

1)Take your functional inputs and generate a model with FDE to create FPC's for each input run to represent the curve. In this case you may not have supplementary values. Make sure that there is a unique identifier for each batch/set of data that you can use later.

2) Export the FPC scores (Save Function Summaries in the FDE Platform) - this will provide you with the FPC scores to test against your output (below) and the ability to profile the FPC scores using the saved prediction formula (use Graph > Profiler and make sure to Expand Intermediate Formulas) - you will use this later for visualising the shape of your inputs.

Use the inputs to model against your output functional shapes:

3) Take the generated FPC scores and align them to the correct batch/row that they are related to in the output time series data (you can use the Join function to update your table).

4) Use your FPC scores as supplementary inputs in the FDE model

5) Create a profiler with the Functional or Wavelet DOE option

6) Create a profiler of the input curves from steps 1 and 2.

This will allow you to generate a model that you can change the FPC scores of the input for and see how they change the shape of the original input (points 1,2) and the output (points 5,6).

Hope this helps, if you have any questions let me know.

Thanks,

Ben

[#4]

Thanks for the detailed steps Ben, much appreciated!