Functional Design of Experiments - Categorical factors

Question

Hello,

Should I use the Functional Design of Experiments in the Functional Data Explorer platform with categorical factors?

I've performed a full factorial DoE with 2 categorical factors and 1 continuous factor (3 levels). My response is a curve (%yield vs three-time points). Should I use the Functional Data Explorer in this case?

Thank you very much!

Mark_Bailey · Accepted Answer

Are you asking if it is advisable or how to do it?

You should be able to analyze your curves as functional responses in principle, but three points are not much of a function. There might not be sufficient detail to warrant FDE versus linear regression. You can include Time as a covariate in the analysis and cross-terms to model interactions between the covariate effect and the factor levels. That is, the function depends on the conditions.

Have you read the documentation about analyzing an experiment with functional responses?

I think it is worth a try!

Ben_BarrIngh · Accepted Answer

Hi Sofia,

You can use 3 time points with the functional data explorer tool if the shape of the curve if the shape of the curve is essential in your understanding. As @Mark_Bailey mentioned, 3 time points does reduce your resolution - but you can still generate models with FDE that give valuable insight if you're happy with it only showing 3 time points.

To show, I've attached an example of simplified growth curve with just 3 time points recorded with a categorical (cell line) and numeric (maltose %) factor and generated a model with the Functional Data Analyser and with the Fit Curve/Curve DoE tool (just click the green script buttons on the left of the data table). The Fit Curve is useful for modelling curves with an expected/pre-determined shape (i.e. sigmoidal, growth/decay) based on your theoretical understanding and can 'smooth' your curves.

Output from a FDE

Output from a Curve DoE with Fit Curve - note how the time series is now smoothed to fit a 'Logistic 3P' sigmoid curve

Let me know if that helps.

Thanks,

Ben