MFPCA: Multilevel functional principal component analysis for...

In ftsa: Functional Time Series Analysis

Multilevel functional principal component analysis for clustering

Description

A multilevel functional principal component analysis for performing clustering analysis

Usage

MFPCA(y, M = NULL, J = NULL, N = NULL)

Arguments

y	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
M	Number of countries
J	Number of functional responses in each country
N	Number of grid points per function

Value

K1	Number of components at level 1
K2	Number of components at level 2
K3	Number of components at level 3
lambda1	A vector containing all level 1 eigenvalues in non-increasing order
lambda2	A vector containing all level 2 eigenvalues in non-increasing order
lambda3	A vector containing all level 3 eigenvalues in non-increasing order
phi1	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
phi2	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
phi3	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
scores1	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
scores2	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.
scores3	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.
mu	A vector containing the overall mean function
eta	A matrix containing the deviation from overall mean function to country-specific mean function. The number of rows is the number of countries
Rj	Common trend
Uij	Country-specific mean function

Author(s)

Chen Tang, Yanrong Yang and Han Lin Shang

See Also

mftsc

ftsa documentation built on Sept. 11, 2023, 5:09 p.m.