mfpca.face: Multilevel functional principal components analysis with fast...

In refund: Regression with Functional Data

Multilevel functional principal components analysis with fast covariance estimation

Description

Decompose dense or sparse multilevel functional observations using multilevel functional principal component analysis with the fast covariance estimation approach.

Usage

mfpca.face(
  Y,
  id,
  visit = NULL,
  twoway = TRUE,
  weight = "obs",
  argvals = NULL,
  pve = 0.99,
  npc = NULL,
  pve2 = NULL,
  npc2 = NULL,
  p = 3,
  m = 2,
  knots = 35,
  silent = TRUE
)

Arguments

Y	A multilevel functional dataset on a regular grid stored in a matrix. Each row of the data is the functional observations at one visit for one subject. Missingness is allowed and need to be labeled as NA. The data must be specified.
id	A vector containing the id information to identify the subjects. The data must be specified.
visit	A vector containing information used to identify the visits. If not provided, assume the visit id are 1,2,... for each subject.
twoway	Logical, indicating whether to carry out twoway ANOVA and calculate visit-specific means. Defaults to TRUE.
weight	The way of calculating covariance. weight = "obs" indicates that the sample covariance is weighted by observations. weight = "subj" indicates that the sample covariance is weighted equally by subjects. Defaults to "obs".
argvals	A vector containing observed locations on the functional domain.
pve	Proportion of variance explained. This value is used to choose the number of principal components for both levels.
npc	Pre-specified value for the number of principal components. If given, this overrides pve.
pve2	Proportion of variance explained in level 2. If given, this overrides the value of pve for level 2.
npc2	Pre-specified value for the number of principal components in level 2. If given, this overrides npc for level 2.
p	The degree of B-splines functions to use. Defaults to 3.
m	The order of difference penalty to use. Defaults to 2.
knots	Number of knots to use or the vectors of knots. Defaults to 35.
silent	Logical, indicating whether to not display the name of each step. Defaults to TRUE.

Details

The fast MFPCA approach (Cui et al., 2023) uses FACE (Xiao et al., 2016) to estimate covariance functions and mixed model equations (MME) to predict scores for each level. As a result, it has lower computational complexity than MFPCA (Di et al., 2009) implemented in the mfpca.sc function, and can be applied to decompose data sets with over 10000 subjects and over 10000 dimensions.

Value

A list containing:

Yhat	FPC approximation (projection onto leading components) of Y, estimated curves for all subjects and visits
Yhat.subject	Estimated subject specific curves for all subjects
Y.df	The observed data
mu	estimated mean function (or a vector of zeroes if center==FALSE).
eta	The estimated visit specific shifts from overall mean.
scores	A matrix of estimated FPC scores for level1 and level2.
efunctions	A matrix of estimated eigenfunctions of the functional covariance, i.e., the FPC basis functions for levels 1 and 2.
evalues	Estimated eigenvalues of the covariance operator, i.e., variances of FPC scores for levels 1 and 2.
pve	The percent variance explained by the returned number of PCs.
npc	Number of FPCs: either the supplied npc, or the minimum number of basis functions needed to explain proportion pve of the variance in the observed curves for levels 1 and 2.
sigma2	Estimated measurement error variance.

Author(s)

Ruonan Li [e-mail], Erjia Cui [e-mail]

References

Cui, E., Li, R., Crainiceanu, C., and Xiao, L. (2023). Fast multilevel functional principal component analysis. Journal of Computational and Graphical Statistics, 32(3), 366-377.

Di, C., Crainiceanu, C., Caffo, B., and Punjabi, N. (2009). Multilevel functional principal component analysis. Annals of Applied Statistics, 3, 458-488.

Xiao, L., Ruppert, D., Zipunnikov, V., and Crainiceanu, C. (2016). Fast covariance estimation for high-dimensional functional data. Statistics and Computing, 26, 409-421.

Examples

data(DTI)
mfpca.DTI <- mfpca.face(Y = DTI$cca, id = DTI$ID, twoway = TRUE)

refund documentation built on Sept. 21, 2024, 1:07 a.m.