MJMbamlss (version 0.1.0)

MFPCA_cov: 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)

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.

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

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)