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I am very new to functional data analysis (FDA). I am reading:

Ramsay, James O., and Silverman, Bernard W. (2006), Functional Data Analysis, 2nd ed., Springer, New York.

However, I am still not very clear where/when to use FDA? Could someone please give me an example especially in medical studies? I really don't know where/when to apply FDA in practice.

For growth curve data, we can use nonlinear mixed models, for longitudinal data, we can use repeated measure ANOVA, and for multivariate data/high dimensional data, we can use PCA, FA, etc. So when/where will be the best timing/situation to use FDA?

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Growth curves are the classical example (Phase and amplitude-based clustering for functional data Slaets L, Claeskens G, Hubert M, 2012, Computational Statistics & Data Analysis, vol. 56, no. 2012, pp. 2360 - 2374.) –  user603 Apr 7 '12 at 22:12
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There are many examples in Applied Functional Data Analysis, by the same authors. –  Vincent Zoonekynd Apr 8 '12 at 10:46
    
many thanks to both of you. I will take a look this AFDA book and CSDA article. –  Tu.2 Apr 8 '12 at 16:34
    
I think you raised a good question because some of the natural situations where functional data analysis can be applied there are the alternative methods that you suggest. –  Michael Chernick May 4 '12 at 15:27
    
I think it depends on the density of your data, whether you consider it closer to repeated measures or a time series - is that wrong? –  rosser Jun 28 '12 at 23:43
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up vote 2 down vote accepted

Functional Data Analysis (FDA) can model phase variation (differences in timing), whereas the alternatives that you mention cannot. An example of phase variation is the variability in timing in the onset of puberty in children. Ignoring phase variation (which is standard practice) mismodels puberty. FDA models phase variation by time warping, where the time axis is locally stretched or compressed to fit a target. In this way, FDA can give a realistic and useful description of the process. FDA requires relatively dense data, but nowadays we see these more and more. In my opinion, FDA has great potential and is vastly underused.

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