A simulated dataset as an example which corresponds to the "practical" case in the paper

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prac is a list with six components (in the given order):

- data
data matrix with three columns: column 1–ID, column 2–measurement, column 3–time.

- eigenfunctions
true eigenfunctions: generated from cubic Bsplines with M=10 equally spaced knots.

- eigenvalues
true eigenvalues: first–1, second–0.66, third–0.52, fourth–0.44, fifth–0.38, others–zero.

- number_of_basis
true number of basis functions: M=10.

- dimension
true dimension of the process: r=5.

- error_sd
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 500 subjects, and each has 2~10 measurements uniformly distributed on [0,1]; in total there are 3018 measurements

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