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?
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.