An example with M=5 (basis functions) and r=3 (non-zero eigenvalues)
A simulated dataset as an example which corresponds to the "easy" case in the paper
easy is a list with six components (in the given order):
data matrix with three columns: column 1–ID, column 2–measurement, column 3–time.
true eigenfunctions: generated from cubic Bsplines with M=5 equally spaced knots.
true eigenvalues: first–1, second–0.66, third–0.52, others–zero.
true number of basis functions: M=5.
true dimension of the process: r=3.
true error standard deviation: 0.25.
mean curve of the process is zero; principal component scores and errors are all i.i.d N(0,1); there are 200 subjects, and each has 2~10 measurements uniformly distributed on [0,1]; in total there are 1227 measurements
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