dot-PACE: Calculate univariate functional PCA

In MFPCA: Multivariate Functional Principal Component Analysis for Data Observed on Different Dimensional Domains

Calculate univariate functional PCA

Description

This function is a slightly adapted version of the fpca.sc function in the refund package for calculating univariate functional principal components based on a smoothed covariance function. The smoothing basis functions are penalized splines.

Usage

.PACE(
  X,
  Y,
  Y.pred = NULL,
  nbasis = 10,
  pve = 0.99,
  npc = NULL,
  makePD = FALSE,
  cov.weight.type = "none"
)

Arguments

X	A vector of xValues.
Y	A matrix of observed functions (by row).
Y.pred	A matrix of functions (by row) to be approximated using the functional principal components. Defaults to NULL, i.e. the prediction is made for the functions in Y.
nbasis	An integer, giving the number of B-spline basis to use. Defaults to 10.
pve	A value between 0 and 1, giving the percentage of variance explained in the data by the functional principal components. This value is used to choose the number of principal components. Defaults to 0.99
npc	The number of principal components to be estimated. Defaults to NULL. If given, this overrides pve.
makePD	Logical, should positive definiteness be enforced for the covariance estimate? Defaults to FALSE.
cov.weight.type	The type of weighting used for the smooth covariance estimate. Defaults to "none", i.e. no weighting. Alternatively, "counts" (corresponds to fpca.sc in refund) weights the pointwise estimates of the covariance function by the number of observation points.

Value

fit	The approximation of Y.pred (if NULL, the approximation of Y) based on the functional principal components.
scores	A matrix containing the estimated scores (observations by row).
mu	The estimated mean function.
efunctions	A matrix containing the estimated eigenfunctions (by row).
evalues	The estimated eigenvalues.
npc	The number of principal comopnents that were calculated.
sigma2	The estimated variance of the measurement error.
estVar	The estimated smooth variance function of the data.

References

Di, C., Crainiceanu, C., Caffo, B., and Punjabi, N. (2009). Multilevel functional principal component analysis. Annals of Applied Statistics, 3, 458–488. Yao, F., Mueller, H.-G., and Wang, J.-L. (2005). Functional data analysis for sparse longitudinal data. Journal of the American Statistical Association, 100, 577–590.

See Also

PACE

MFPCA documentation built on Sept. 15, 2022, 9:07 a.m.