%% $Id: mvrVal.Rd 117 2007-06-26 12:57:53Z bhm $\encoding{latin1}\name{mvrVal}\alias{MSEP}\alias{MSEP.mvr}\alias{RMSEP}\alias{RMSEP.mvr}\alias{R2}\alias{mvrValstats}\title{MSEP, RMSEP and R2 of PLSR and PCR models}\description{  Functions to estimate the mean squared error of prediction (MSEP),  root mean squared error of prediction (RMSEP) and \eqn{R^2}  (A.K.A. coefficient of multiple determination) for fitted  PCR and PLSR models.  Test-set, cross-validation and calibration-set  estimates are implemented.}\usage{MSEP(object, ...)\method{MSEP}{mvr}(object, estimate, newdata, ncomp = 1:object$ncomp, comps,     intercept = cumulative, se = FALSE, \dots)RMSEP(object, ...)\method{RMSEP}{mvr}(object, ...)R2(object, 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 Bj鴕n-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}