mfpca_vd: Multivariate functional principal component analysis for...
In VDPO: Working with and Analyzing Functional Data of Varying Lengths

mfpca_vd

R Documentation

Multivariate functional principal component analysis for variable domain data

Description

Performs a multivariate functional principal component analysis (MFPCA) for functional data observed on subject-specific (variable) domains. Each functional variable is first decomposed through a variable domain FPCA, and the resulting univariate scores are combined into a domain-varying multivariate decomposition.

Usage

mfpca_vd(
  Data,
  Times = NULL,
  M_grid = NULL,
  Hz = 1,
  m_npcs = NULL,
  u_npcs = 5,
  k_m = 15,
  model_type = "gam"
)

Arguments

`Data`	A list (one entry per functional variable) of matrices with subjects in rows and observation points in columns, with `NA` on the unobserved part of each domain. All variables must have the same number of subjects. Currently two variables are supported.
`Times`	A list of matrices, the same shape as `Data`, giving the actual observation time of each measurement. Mutually exclusive with `M_grid`.
`M_grid`	A numeric vector of length `N` with the domain length of each subject, used when the observations are equidistant. Mutually exclusive with `Times`.
`Hz`	Sampling rate used to build the equidistant grid when `M_grid` is supplied (default `1`).
`m_npcs`	Number of multivariate principal components to retain. If `NULL`, the number explaining more than 90 percent of the variance is used.
`u_npcs`	Number of univariate principal components retained per variable (default `5`).
`k_m`	Dimension of the basis used to model the score covariances along the domain (default `15`).
`model_type`	Either `"gam"` (the default) or `"sop"`, the method used to smooth the score covariances along the domain.

Details

The observation times can be supplied in two mutually exclusive ways. With Times, each variable carries a matrix (subjects in rows, observation points in columns) holding the actual observation time of every measurement, and the domain of subject i is taken as the maximum observed time. With M_grid, the observations are assumed equidistant and M_grid is a vector of length N giving the domain length of each subject, so subject i is evaluated on seq(0, M_grid[i], by = 1 / Hz). Exactly one of Times or M_grid must be provided.

Value

A list with the following items:

scores_m: Matrix of multivariate scores.
efunctions_m: Multivariate eigenfunctions, as a list over domains, each a list over variables.
efunctions_u: Univariate eigenfunctions, as a list over variables.
scores_u: Matrix of univariate scores.
evalues_u: Univariate eigenvalues, as a list over variables.
evalues_m: Multivariate eigenvalues, as a list over domains.
var_u: Cumulative variance explained by the univariate components.
mean_model: The fitted univariate mean models (one per variable).
M_grid: The domain grid used.
argvals_u: The observation times of each subject, as a list over variables, each a list over subjects.