dot-PACE function

Calculate univariate functional PCA

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.

.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.

Returns

• 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