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%% $Id$
\encoding{UTF-8}
\name{mvrVal}
\alias{MSEP}
\alias{MSEP.mvr}
\alias{RMSEP}
\alias{RMSEP.mvr}
\alias{R2}
\alias{R2.mvr}
\alias{mvrValstats}
\title{MSEP, RMSEP and R2 of PLSR and PCR models}
\description{
Functions to estimate the mean squared error of prediction (MSEP),
root mean squared error of prediction (RMSEP) and \eqn{R^2}
(A.K.A. coefficient of multiple determination) for fitted
PCR and PLSR models. Test-set, cross-validation and calibration-set
estimates are implemented.
}
\usage{
MSEP(object, ...)
\method{MSEP}{mvr}(object, estimate, newdata, ncomp = 1:object$ncomp, comps,
intercept = cumulative, se = FALSE, \dots)
RMSEP(object, ...)
\method{RMSEP}{mvr}(object, ...)
R2(object, ...)
\method{R2}{mvr}(object, estimate, newdata, ncomp = 1:object$ncomp, comps,
intercept = cumulative, se = FALSE, \dots)
mvrValstats(object, estimate, newdata, ncomp = 1:object$ncomp, comps,
intercept = cumulative, se = FALSE, \dots)
}
\arguments{
\item{object}{an \code{mvr} object}
\item{estimate}{a character vector. Which estimators to use.
Should be a subset of \code{c("all", "train", "CV", "adjCV",
"test")}. \code{"adjCV"} is only available for (R)MSEP. See
below for how the estimators are chosen.}
\item{newdata}{a data frame with test set data.}
\item{ncomp, comps}{a vector of positive integers. The components or number
of components to use. See below.}
\item{intercept}{logical. Whether estimates for a model with zero
components should be returned as well.}
\item{se}{logical. Whether estimated standard errors of the estimates
should be calculated. Not implemented yet.}
\item{\dots}{further arguments sent to underlying functions or (for
\code{RMSEP}) to \code{MSEP}}
}
\details{
\code{RMSEP} simply calls \code{MSEP} and takes the square root of the
estimates. It therefore accepts the same arguments as \code{MSEP}.
Several estimators can be used. \code{"train"} is the training
or calibration data estimate, also called (R)MSEC. For \code{R2},
this is the unadjusted \eqn{R^2}. It is
overoptimistic and should not be used for assessing models.
\code{"CV"} is the cross-validation estimate, and \code{"adjCV"} (for
\code{RMSEP} and \code{MSEP}) is
the bias-corrected cross-validation estimate. They can only be
calculated if the model has been cross-validated.
Finally, \code{"test"} is the test set estimate, using \code{newdata}
as test set.
Which estimators to use is decided as follows (see below for
\code{mvrValstats}). If
\code{estimate} is not specified, the test set estimate is returned if
\code{newdata} is specified, otherwise the CV and adjusted CV (for
\code{RMSEP} and \code{MSEP})
estimates if the model has been cross-validated, otherwise the
training data estimate. If \code{estimate} is \code{"all"}, all
possible estimates are calculated. Otherwise, the specified estimates
are calculated.
Several model sizes can also be specified. If \code{comps} is missing
(or is \code{NULL}), \code{length(ncomp)} models are used, with
\code{ncomp[1]} components, \ldots, \code{ncomp[length(ncomp)]}
components. Otherwise, a single model with the components
\code{comps[1]}, \ldots, \code{comps[length(comps)]} is used.
If \code{intercept} is \code{TRUE}, a model with zero components is
also used (in addition to the above).
The \eqn{R^2} values returned by \code{"R2"} are calculated as \eqn{1
- SSE/SST}, where \eqn{SST} is the (corrected) total sum of squares
of the response, and \eqn{SSE} is the sum of squared errors for either
the fitted values (i.e., the residual sum of squares), test set
predictions or cross-validated predictions (i.e., the \eqn{PRESS}).
For \code{estimate = "train"}, this is equivalent to the squared
correlation between the fitted values and the response. For
\code{estimate = "train"}, the estimate is often called the prediction
\eqn{R^2}.
\code{mvrValstats} is a utility function that calculates the
statistics needed by \code{MSEP} and \code{R2}. It is not intended to
be used interactively. It accepts the same arguments as \code{MSEP}
and \code{R2}. However, the \code{estimate} argument must be
specified explicitly: no partial matching and no automatic choice is
made. The function simply calculates the types of estimates it knows,
and leaves the other untouched.
}
%\value{
\section{Value}{
\code{mvrValstats} returns a list with components
\describe{
\item{SSE}{three-dimensional array of SSE values. The first dimension
is the different estimators, the second is the response variables
and the third is the models.}
\item{SST}{matrix of SST values. The first dimension
is the different estimators and the second is the response
variables.}
\item{nobj}{a numeric vector giving the number of objects used for
each estimator.}
\item{comps}{the components specified, with \code{0} prepended if
\code{intercept} is \code{TRUE}.}
\item{cumulative}{\code{TRUE} if \code{comps} was \code{NULL} or not
specified.}
}
The other functions return an object of class \code{"mvrVal"}, with
components
\describe{
\item{val}{three-dimensional array of estimates. The first dimension
is the different estimators, the second is the response variables
and the third is the models.}
\item{type}{\code{"MSEP"}, \code{"RMSEP"} or \code{"R2"}.}
\item{comps}{the components specified, with \code{0} prepended if
\code{intercept} is \code{TRUE}.}
\item{cumulative}{\code{TRUE} if \code{comps} was \code{NULL} or not
specified.}
\item{call}{the function call}
}
}
\references{
Mevik, B.-H., Cederkvist, H. R. (2004) Mean Squared Error of
Prediction (MSEP) Estimates for Principal Component Regression (PCR)
and Partial Least Squares Regression (PLSR).
\emph{Journal of Chemometrics}, \bold{18}(9), 422--429.
}
\author{Ron Wehrens and Bjørn-Helge Mevik}
\seealso{\code{\link{mvr}}, \code{\link{crossval}}, \code{\link{mvrCv}},
\code{\link{validationplot}}, \code{\link{plot.mvrVal}}}
\examples{
data(oliveoil)
mod <- plsr(sensory ~ chemical, ncomp = 4, data = oliveoil, validation = "LOO")
RMSEP(mod)
\dontrun{plot(R2(mod))}
}
\keyword{regression}
\keyword{multivariate}
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