Description Usage Arguments Details Value Author(s) References Examples
Decomposes functional observations using functional principal components analysis. A mixed model framework is used to estimate scores and obtain variance estimates.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 
Y, 
The user must supply a matrix of functions on a regular grid 
id 
Must be supplied, a vector containing the id information used to identify clusters 
visit 
A vector containing information used to identify visits. Defaults to 
twoway 
logical, indicating whether to carry out twoway ANOVA and calculate visitspecific means. Defaults to 
argvals 
function argument. 
nbasis 
number of Bspline basis functions used for estimation of the mean function and bivariate smoothing of the covariance surface. 
pve 
proportion of variance explained: used to choose the number of principal components. 
npc 
prespecified value for the number of principal components (if
given, this overrides 
makePD 
logical: should positive definiteness be enforced for the
covariance surface estimate? Defaults to 
center 
logical: should an estimated mean function be subtracted from

cov.est.method 
covariance estimation method. If set to 
integration 
quadrature method for numerical integration; only

This function computes a multilevel FPC decomposition for a set of observed curves, which may be sparsely observed and/or measured with error. A mixed model framework is used to estimate level 1 and level 2 scores.
MFPCA was proposed in Di et al. (2009), with variations for
MFPCA with sparse data in Di et al. (2014).
mfpca.sc
uses penalized splines to smooth the covariance functions, as
Described in Di et al. (2009) and Goldsmith et al. (2013).
An object of class mfpca
containing:
Yhat 
FPC approximation (projection onto leading components)
of 
Yhat.subject 
estimated subject specific curves for all subjects 
Y 
the observed data 
scores 
n \times npc matrix of estimated FPC scores for level1 and level2. 
mu 
estimated mean
function (or a vector of zeroes if 
efunctions

d \times npc 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. 
npc 
number of FPCs: either the supplied 
sigma2 
estimated measurement error variance. 
eta 
the estimated visit specific shifts from overall mean. 
Julia Wrobel jw3134@cumc.columbia.edu, Jeff Goldsmith jeff.goldsmith@columbia.edu, and Chongzhi Di
Di, C., Crainiceanu, C., Caffo, B., and Punjabi, N. (2009). Multilevel functional principal component analysis. Annals of Applied Statistics, 3, 458–488.
Di, C., Crainiceanu, C., Caffo, B., and Punjabi, N. (2014). Multilevel sparse functional principal component analysis. Stat, 3, 126–143.
Goldsmith, J., Greven, S., and Crainiceanu, C. (2013). Corrected confidence bands for functional data using principal components. Biometrics, 69(1), 41–51.
1 2 3 4 5 6 7 8 
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.