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\encoding{UTF-8}
\name{svdpc.fit}
\alias{svdpc.fit}
\title{Principal Component Regression}
\description{Fits a PCR model using the singular value decomposition.}
\usage{svdpc.fit(X, Y, ncomp, center = TRUE, stripped = FALSE, \dots)}
\arguments{
\item{X}{a matrix of observations. \code{NA}s and \code{Inf}s are not
allowed.}
\item{Y}{a vector or matrix of responses. \code{NA}s and \code{Inf}s
are not allowed.}
\item{ncomp}{the number of components to be used in the
modelling.}
\item{center}{logical, determines if the \eqn{X} and \eqn{Y} matrices
are mean centered or not. Default is to perform mean centering.}
\item{stripped}{logical. If \code{TRUE} the calculations are stripped
as much as possible for speed; this is meant for use with
cross-validation or simulations when only the coefficients are
needed. Defaults to \code{FALSE}.}
\item{\dots}{other arguments. Currently ignored.}
}
\details{This function should not be called directly, but through
the generic functions \code{pcr} or \code{mvr} with the argument
\code{method="svdpc"}. The singular value decomposition is
used to calculate the principal components.
}
\value{A list containing the following components is returned:
\item{coefficients}{an array of regression coefficients for 1, \ldots,
\code{ncomp} components. The dimensions of \code{coefficients} are
\code{c(nvar, npred, ncomp)} with \code{nvar} the number
of \code{X} variables and \code{npred} the number of variables to be
predicted in \code{Y}.}
\item{scores}{a matrix of scores.}
\item{loadings}{a matrix of loadings.}
\item{Yloadings}{a matrix of Y-loadings.}
\item{projection}{the projection matrix used to convert X to scores.}
\item{Xmeans}{a vector of means of the X variables.}
\item{Ymeans}{a vector of means of the Y variables.}
\item{fitted.values}{an array of fitted values. The dimensions of
\code{fitted.values} are \code{c(nobj, npred, ncomp)} with
\code{nobj} the number samples and \code{npred} the number of
Y variables.}
\item{residuals}{an array of regression residuals. It has the same
dimensions as \code{fitted.values}.}
\item{Xvar}{a vector with the amount of X-variance explained by each
component.}
\item{Xtotvar}{Total variance in \code{X}.}
If \code{stripped} is \code{TRUE}, only the components
\code{coefficients}, \code{Xmeans} and \code{Ymeans} are returned.
}
\references{
Martens, H., Næs, T. (1989) \emph{Multivariate calibration.}
Chichester: Wiley.
}
\author{Ron Wehrens and Bjørn-Helge Mevik}
\seealso{
\code{\link{mvr}}
\code{\link{plsr}}
\code{\link{pcr}}
\code{\link{cppls}}
}
\keyword{regression}
\keyword{multivariate}
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