\name{AmpPhaseDecomp}
\alias{AmpPhaseDecomp}
\title{
Decomposition for Amplitude and Phase Variation
}
\description{
Registration is the process of aligning peaks, valleys and other
features in a sample of curves. Once the registration has taken
place, this function computes two mean squared error measures, one for
amplitude variation, and the other for phase variation. It also
computes a squared multiple correlation index of the amount of
variation in the unregistered functions is due to phase.
}
\usage{
AmpPhaseDecomp(xfd, yfd, hfd, rng=xrng)
}
\arguments{
\item{xfd}{
a functional data object containing the unregistered curves.
}
\item{yfd}{
a functional data object containing the registered curves.
}
\item{hfd}{
a functional data object containing the strictly monotone warping
functions $h(t)$. This is typically returned by the functions
\code{landmarkreg} and \code{register.fd}.
}
\item{rng}{
a vector of length 2 specifying a range of values over which the
decomposition is to be computed. Both values must be within the
range of the functional data objects in the argument. By default
the whole range of the functional data objects is used.
}
}
\details{
The decomposition can yield negative values for \code{MS.phas} if the
registration does not improve the alignment of the curves, or if used
to compare two registration processes based on different principles,
such as is the case for functions \code{landmarkreg} and
\code{register.fd}.
}
\value{
a named list with the following components:
\item{MS.amp}{
the mean squared error for amplitude variation.
}
\item{MS.phas}{
the mean squared error for phase variation.
}
\item{RSQR}{
the squared correlation measure of the proportion of the total
variation that is due to phase variation.
}
\item{C}{
a constant required for the decomposition. Its value is one if the
derivatives the warping functions are independent of the squared
registered functions.
}
}
\seealso{
\code{\link{landmarkreg}},
\code{\link{register.fd}},
\code{\link{smooth.morph}}
}
\examples{
#See the analysis for the growth data in the examples.
}
% docclass is function
\keyword{smooth}
\keyword{models}