MFPCA_cov {MJMbamlss}

Function to calculate the multivariate FPCA for a given covariance matrix and univariate basis functions

Description

Function to calculate the multivariate FPCA for a given covariance matrix and univariate basis functions

Usage

MFPCA_cov(cov, basis_funs, scores = NULL, weights = NULL)

Arguments

cov

Covariance matrix of the basis functions coefficients.

basis_funs

List with basis functions on each dimension. The basis functions are funData objects

scores

Matrix (n rows, B columns) containing the basis functions coefficients. Defaults to NULL which does not calculate the multivariate scores.

weights

Vector of weights, defaults to 1 for each element

Value

List mimicking an MFPCAfit object containing the following components:

values

A vector of eigenvalues.

functions

A multiFunData object containing the multivariate functional principal components.

scores

A matrix containing the scores (if applicable).

vectors

A matrix representing the eigenvectors associated with the combined univaraite score vectors.

normFactors

The normalizing factors used for calculating the multivariate eigenfunctions and scores.

Examples

library(funData)
# Covariance matrix for the data generation in simulation scenario I
auto <- matrix(c(0.08, -0.07, -0.07, 0.9), ncol = 2)
cross <- matrix(rep(0.03, 4), ncol = 2)
cor <- matrix(c(0, 1, 0.75, 0.5, 0, 0,
                1, 0, 1, 0.75, 0.5, 0,
                0.75, 1, 0, 1, 0.75, 0.5,
                0.5, 0.75, 1, 0, 1, 0.75,
                0, 0.5, 0.75, 1, 0, 1,
                0, 0, 0.5, 0.75, 1, 0),
               ncol = 6)
cov <- kronecker(cor, cross) + kronecker(diag(c(1, 1.2, 1.4, 1.6, 1.8, 2)),
                                         auto)
# Basis functions on each dimension
seq1 <- seq(0, 1, by = 0.01)
b_funs <- rep(list(funData(argvals = seq1,
              X = matrix(c(rep(1, length(seq1)), seq1),
              byrow = TRUE, ncol = length(seq1)))), 6)
# Prepare objects for the model on different data sets
mfpca_tru <- MFPCA_cov(cov = cov, basis_funs = b_funs)