A multilevel functional principal component analysis for performing clustering analysis
MFPCA(y, M = NULL, J = NULL, N = NULL)Number of components at level 1
Number of components at level 2
Number of components at level 3
A vector containing all level 1 eigenvalues in non-increasing order
A vector containing all level 2 eigenvalues in non-increasing order
A vector containing all level 3 eigenvalues in non-increasing order
A matrix containing all level 1 eigenfunctions. Each row contains an eigenfunction evaluated at the same set of grid points as the input data. The eigenfunctions are in the same order as the corresponding eigenvalues
A matrix containing all level 2 eigenfunctions. Each row contains an eigenfunction evaluated at the same set of grid points as the input data. The eigenfunctions are in the same order as the corresponding eigenvalues
A matrix containing all level 3 eigenfunctions. Each row contains an eigenfunction evaluated at the same set of grid points as the input data. The eigenfunctions are in the same order as the corresponding eigenvalues
A matrix containing estimated level 1 principal component scores. Each row corresponds to the level 1 scores for a particular subject in a cluster. The number of rows is the same as that of the input matrix y. Each column contains the scores for a level 1 component for all subjects
A matrix containing estimated level 2 principal component scores. Each row corresponds to the level 2 scores for a particular subject in a cluster. The number of rows is the same as that of the input matrix y. Each column contains the scores for a level 2 component for all subjects.
A matrix containing estimated level 3 principal component scores. Each row corresponds to the level 3 scores for a particular subject in a cluster. The number of rows is the same as that of the input matrix y. Each column contains the scores for a level 3 component for all subjects.
A vector containing the overall mean function
A matrix containing the deviation from overall mean function to country-specific mean function. The number of rows is the number of countries
Common trend
Country-specific mean function
A data matrix containing functional responses. Each row contains measurements from a function at a set of grid points, and each column contains measurements of all functions at a particular grid point
Number of countries
Number of functional responses in each country
Number of grid points per function
Chen Tang, Yanrong Yang and Han Lin Shang
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