fitted.FPCA | R Documentation |
Combines the zero-meaned fitted values and the interpolated mean to get the fitted values for the trajectories
or the derivatives of these trajectories.
Estimates are given on the work-grid, not on the observation grid. Use ConvertSupport
to map the estimates to your desired domain. 100*(1-alpha)
-percentage coverage intervals, or
bands, for trajectory estimates (not derivatives) are provided. For details consult the example.
## S3 method for class 'FPCA' fitted( object, K = NULL, derOptns = list(p = 0), ciOptns = list(alpha = NULL, cvgMethod = NULL), ... )
object |
A object of class FPCA returned by the function FPCA(). |
K |
The integer number of the first K components used for the representation. (default: length(fpcaObj$lambda )) |
derOptns |
A list of options to control the derivation parameters specified by |
ciOptns |
A list of options to control the confidence interval/band specified by |
... |
Additional arguments |
Available derivation control options are
The order of the derivatives returned (default: 0, max: 2)
The method used to produce the sample of derivatives ('FPC' (default) or 'QUO'). See Liu and Müller (2009) for more details
Bandwidth for smoothing the derivatives (default: p * 0.10 * S)
Smoothing kernel choice; same available types are FPCA(). default('epan')
Available confidence interval/band control options are
Significant level for confidence interval/band for trajectory coverage. default=0.05 (currently only work when p=0)
Option for trajectory coverage method between 'interval' (pointwise coverage) and 'band' (simultaneous coverage). default='band'
If alpha
is NULL
, p>1
or functional observations are dense, an n
by length(workGrid)
matrix, each row of which contains a sample. Otherwise, it returns a list which consists of the following items:
workGrid |
An evaluation grid for fitted values. |
fitted |
An n by length(workGrid) matrix, each row of which contains a sample. |
cvgUpper |
An n by length(workGrid) matrix, each row of which contains the upper |
cvgLower |
An n by length(workGrid) matrix, each row of which contains the lower |
Yao, F., Müller, H.-G. and Wang, J.-L. "Functional data analysis for sparse longitudinal data", Journal of the American Statistical Association, vol.100, No. 470 (2005): 577-590.
Liu, Bitao, and Hans-Georg Müller. "Estimating derivatives for samples of sparsely observed functions, with application to online auction dynamics." Journal of the American Statistical Association 104, no. 486 (2009): 704-717. (Sparse data FPCA)
set.seed(1) n <- 100 pts <- seq(0, 1, by=0.05) sampWiener <- Wiener(n, pts) sampWiener <- Sparsify(sampWiener, pts, 5:10) res <- FPCA(sampWiener$Ly, sampWiener$Lt, list(dataType='Sparse', error=FALSE, kernel='epan', verbose=TRUE)) fittedY <- fitted(res, ciOptns = list(alpha=0.05)) workGrid <- res$workGrid cvgUpper <- fittedY$cvgUpper cvgLower <- fittedY$cvgLower op <- par(mfrow=c(2,3)) ind <- sample(1:n,6) for (i in 1:6) { j <- ind[i] plot(workGrid,cvgUpper[j,],type='l',ylim=c(min(cvgLower[j,]),max(cvgUpper[j,])),col=4,lty=2, xlab='t', ylab='X(t)', main=paste(j,'-th subject',sep='')) points(workGrid,cvgLower[j,],type='l',col=4,lty=2) points(res$inputData$Lt[[j]],res$inputData$Ly[[j]]) } par(op)
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