FDE model selection and fit. A 'Knotty' problem...

[#1]

Hi All,

I'm currently trying to explore some analytical data where the response changes over time using FDE.

The context is that this is an analytical method where the response of the same sample(s) are changing over time. We used a surface-response DoE design in an attempt to capture the effect of the 2 main factors and identify what is causing this change.

For each experiment in the design, we added multiple replicates to generate a time-series for each experiment. This was then analysed using FDE.

The attached image shows the b-spline fit of the data. My monkey brain sees a very obvious oscillating pattern here. The fit is obviously not great, and I am unable to increase the Knots past 5 (as it was suggested to try 12-13 to try to capture each inflection point), but I can't figure out how to do it; so any help on that would be appreciated.

My question is, what do you think will be the best approach to analyse this data? The end point is to identify conditions that prevent the changing response over time.

I've considered normalising the time-series data to remove the oscillation, but worry I'll lose some resolution there. I'm also unable to increase the sampling frequency due to the 'run' time. 

Thanks!

[#2]

The selection of the fit is based on the model selection criterion and review of the individual functions. The fit of the individual functions looks pretty good. The red line plotted in the overlay of all the functions is the mean function.

The individual functions look nothing like the overlay. That is to say, I do not see oscillations in any of the individual functions. Are they segments of the domain?

If the functions truly oscillate, then a Fourier basis might perform better. The assumption is that each function represents one cycle of action, though a cycle might exhibit more than one oscillation.

[#3]

Hi Mark,

Thanks for the response. 

I am not expecting any cyclical response in the data, more a decreasing trend with varying slopes depending on the conditions. If you think the fit is good, then i'm happy to defer to your experience and accept my data!

I thought it best to seek expert opinion given my unfamiliarity with FDE.

Thanks!

[#4]

Please post a picture of the lower section of FDE that contains the function principal components. That would help me help you assess the fit and usefulness of the basis expansion.