fdapace (version 0.1.1)

FPCA: Functional Principal Component Analysis

Description

FPCA for dense or sparse functional data.

Usage

FPCA(y, t, optns = list())

Arguments

y

A list of n vectors containing the observed values for each individual. Missing values specified by NAs are supported for dense case (dataType='dense').

t

A list of n vectors containing the observation time points for each individual corresponding to y.

optns

A list of options control parameters specified by list(name=value). See `Details'.

Value

• A list containing the following fields:
• sigma2
  Variance for measure error.
• lambda
  A vector of length K containing eigenvalues.
• phi
  An nWorkGrid by K matrix containing eigenfunctions, supported on workGrid.
• xiEst
  A n by K matrix containing the FPC estimates.
• xiVar
  A list of length n, each entry containing the variance estimates for the FPC estimates.
• obsGrid
  The (sorted) grid points where all observation points are pooled.
• mu
  A vector of length nObsGrid containing the mean function estimate.
• workGrid
  A vector of length nWorkGrid. The internal regular grid on which the eigen analysis is carried on.
• smoothedCov
  A nWorkGrid by nWorkGrid matrix of the smoothed covariance surface.
• fittedCov
  A nWorkGrid by nWorkGrid matrix of the fitted covariance surface, which is guaranteed to be non-negative definite.
• optns
  A list of actually used options.
• bwMu
  The selected (or user specified) bandwidth for smoothing the mean function.
• bwCov
  The selected (or user specified) bandwidth for smoothing the covariance function.
• rho
  A regularizing scalar for the measurement error variance estimate.
• cumFVE
  A vector with the percentages of the total variance explained by each FPC. Increase to almost 1.
• FVE
  A percentage indicating the total variance explained by chosen FPCs with corresponding 'FVEthreshold'.
• criterionValue
  A scalar specifying the criterion value obtained by the selected number of components with specific methodSelectK: FVE,AIC,BIC values or NULL for fixedK.
• inputData
  A list containting the original 'y' and 't' lists used as inputs to FPCA. NULL if 'lean' was specified to be TRUE.

Details

Available control options are [object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

References

Yao, F., Mueller, H.G., Clifford, A.J., Dueker, S.R., Follett, J., Lin, Y., Buchholz, B., Vogel, J.S. (2003). "Shrinkage estimation for functional principal component scores, with application to the population kinetics of plasma folate." Biometrics 59, 676-685. (Shrinkage estimates for dense data)

Yao, Fang, Hans-Georg Mueller, and Jane-Ling Wang. "Functional data analysis for sparse longitudinal data." Journal of the American Statistical Association 100, no. 470 (2005): 577-590. (Sparse data FPCA)

Liu, Bitao, and Hans-Georg Mueller. "Estimating derivatives for samples of sparsely observed functions, with application to online auction dynamics." Journal of the American Statistical Association 104, no. 486 (2009): 704-717. (Sparse data FPCA)

Castro, P. E., W. H. Lawton, and E. A. Sylvestre. "Principal modes of variation for processes with continuous sample curves." Technometrics 28, no. 4 (1986): 329-337. (Dense data FPCA)

Examples

set.seed(1)
n <- 20
pts <- seq(0, 1, by=0.05)
sampWiener <- Wiener(n, pts)
sampWiener <- Sparsify(sampWiener, pts, 10)
res <- FPCA(sampWiener$yList, sampWiener$tList, 
            list(dataType='Sparse', error=FALSE, kernel='epan', verbose=TRUE))
CreateCovPlot(res, 'Fitted')