.PACE {MFPCA} | R Documentation |
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 |
nbasis |
An integer, giving the number of B-spline basis to use.
Defaults to |
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 |
npc |
The number of principal components to be estimated. Defaults to
|
makePD |
Logical, should positive definiteness be enforced for the
covariance estimate? Defaults to |
cov.weight.type |
The type of weighting used for the smooth covariance
estimate. Defaults to |
Value
fit |
The approximation of |
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.