An elegant application of Functional Data Analysis is to model longitudinal data as a curve and then study the curve’s dynamics. For example, in pharmacokinetics and other medical studies analyzing multiple measurements of drug or protein concentrations in blood samples, it may be interest to determine if the concentrations in subjects undergoing one type of treatment rise quicker than those undergoing an alternative treatment. In this post, I will generate some plausible fake data for measurements taken over time for two groups of subjects, use the techniques of Functional Data Analysis to represent these data as a continuous curve for each subject, and look at some of the dynamic properties of the curves, in particular their velocities and accelerations.
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This is a companion discussion topic for the original entry at https://rviews.rstudio.com/2021/10/14/fda-and-the-dynamics-of-curves