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Custom DOE with Principle components or Functional principle components as covariates?

frankderuyck

I constructed custom DOE's with principle components and fuctional principle components as covariates and for both got equivalent good models. The FDE is really an excellent tool however is there a benefit for using functional principle components over regular PC's for setting up a covariate custom DOE? Are both equivalent?

Accepted answers

Phil_Kay

Thanks, @frankderuyck . That makes sense.

Yes, if your functional data has all observations aligned in the X-dimension (time or wavenumber) then you could use regular PCA or functional PCA and I would expect that you will get just as good a model fit.

However, there may be an advantage in using FDE in that you could ultimately find which functional PCs correlate with your DoE response and then visualise the shape of the function for a given value of the response, for example the best or worst cases.

I think there is probably an advantage in interpretation using FDE versus regular PCA.

In cases where the functional data does not have observations aligned in the X-dimension you will not be able to use regular PCA, unless you do a lot of work to create aligned observations by interpolation.

All comments

Phil_Kay

Hi @frankderuyck,

That sounds like a really interesting application of Functional Data Explorer.

Your question:

"...is there a benefit for using functional principle components over regular PC's for setting up a covariate custom DOE? Are both equivalent?"

I think this will depend very much on what the principal components (regular and functional) are on.

Regards,

Phil

frankderuyck

Hi Phil, could you clarify your answer with an example?

Phil_Kay

Hi,

It would be great if you could say more about your actual example. What are you using functional and regular PCs to describe?

It is very difficult to provide an example. But there will be situations where regular PCA is not useful for summarising a covariate. For example, if the covariate is a time series of a sensor logging a variable for each batch through a process and the sampling is irregular in the time dimension.

Regards,
Phil

frankderuyck

Phil, my case is about predicting a component concentration in a mixture by spectra. Spectra are functions which are correlated over the different mixture samples, I guess in this case both PCA and FPCA can be used? If I understand well, in case that the functions are not correlated like e.g. process time series it is better to us FPCA?