%% $Id: mvr.Rd 132 2007-08-24 09:21:05Z bhm $\encoding{latin1}\name{mvr}\alias{mvr}\alias{pcr}\alias{plsr}\title{Partial Least Squares and Principal Component Regression}\description{  Functions to perform partial least squares regression (PLSR) or  principal component regression (PCR), with a formula interface.  Cross-validation can be used.  Prediction, model extraction, plot,  print and summary methods exist.}%% FIXME: Maybe use a \synopsis section, and show typical uses in \usage:\usage{mvr(formula, ncomp, data, subset, na.action,    method = pls.options()$mvralg,    scale = FALSE, validation = c("none", "CV", "LOO"),    model = TRUE, x = FALSE, y = FALSE, \dots)plsr(\dots, method = pls.options()$plsralg)pcr(\dots, method = pls.options()$pcralg)}\arguments{  \item{formula}{a model formula.  Most of the \code{lm} formula    constructs are supported.  See below.}  \item{ncomp}{the number of components to include in the model (see below).}  \item{data}{an optional data frame with the data to fit the model from.}  \item{subset}{an optional vector specifying a subset of observations    to be used in the fitting process.}  \item{na.action}{a function which indicates what should happen when    the data contain missing values.}  \item{method}{the multivariate regression method to be used.  If    \code{"model.frame"}, the model frame is returned.}  \item{scale}{numeric vector, or logical.  If numeric vector, \eqn{X}    is scaled by dividing each variable with the corresponding element    of \code{scale}.  If \code{scale} is \code{TRUE}, \eqn{X} is scaled    by dividing each variable by its sample standard deviation.  If    cross-validation is selected, scaling by the standard deviation is    done for every segment.}  \item{validation}{character.  What kind of (internal) validation to    use.  See below.}  \item{model}{a logical.  If \code{TRUE}, the model frame is returned.}  \item{x}{a logical.  If \code{TRUE}, the model matrix is returned.}  \item{y}{a logical.  If \code{TRUE}, the response is returned.}  \item{\dots}{additional arguments, passed to the underlying fit    functions, and \code{mvrCv}.}}\details{  The functions fit PLSR or PCR models with 1, \eqn{\ldots},  \code{ncomp} number of components.  Multi-response models are fully  supported.  The type of model to fit is specified with the \code{method}  argument. Four PLSR algorithms are available: the kernel algorithm  (\code{"kernelpls"}), the wide kernel algorithm (\code{"widekernelpls"}),  SIMPLS (\code{"simpls"}) and the classical  orthogonal scores algorithm (\code{"oscorespls"}).  One PCR algorithm  is available: using the singular value decomposition (\code{"svdpc"}).  If \code{method} is \code{"model.frame"}, the model frame is returned.  The functions \code{pcr} and \code{plsr} are wrappers for \code{mvr},  with different values for \code{method}.  The \code{formula} argument should be a symbolic formula of the form  \code{response ~ terms}, where \code{response} is the name of the  response vector or matrix (for multi-response models) and \code{terms}  is the name of one or more predictor matrices, usually separated by  \code{+}, e.g., \code{water ~ FTIR} or \code{y ~ X + Z}.  See  \code{\link{lm}} for a detailed description.  The named  variables should exist in the supplied \code{data} data frame or in  the global environment.  Note: Do not use \code{mvr(mydata$y ~    mydata$X, \ldots)}, instead use \code{mvr(y ~ X, data = mydata,    \ldots)}.  Otherwise, \code{\link{predict.mvr}} will not work properly.  The chapter \samp{Statistical models in R} of the manual \samp{An    Introduction to R} distributed with \R is a good reference on  formulas in \R.  The number of components to fit is specified with the argument  \code{ncomp}.  It this is not supplied, the maximal number of  components is used (taking account of any cross-validation).  If \code{validation = "CV"}, cross-validation is performed.  The number and  type of cross-validation segments are specified with the arguments  \code{segments} and \code{segment.type}.  See \code{\link{mvrCv}} for  details.  If \code{validation = "LOO"}, leave-one-out cross-validation  is performed.  It is an error to specify the segments when  \code{validation = "LOO"} is specified.  Note that the cross-validation is optimised for speed, and some  generality has been sacrificed.  Especially, the model matrix is  calculated only once for the complete cross-validation, so models like  \code{y ~ msc(X)} will not be properly cross-validated.  However,  scaling requested by \code{scale = TRUE} is properly cross-validated.  For proper cross-validation of models where the model matrix must be  updated/regenerated for each segment, use the separate function  \code{\link{crossval}}.}\value{  If \code{method = "model.frame"}, the model frame is returned.  Otherwise, an object of class \code{mvr} is returned.  The object contains all components returned by the underlying fit  function.  In addition, it contains the following components:  \item{validation}{if validation was requested, the results of the    cross-validation.  See \code{\link{mvrCv}} for details.}  \item{na.action}{if observations with missing values were removed,    \code{na.action} contains a vector with their indices.  The    class of this vector is used by functions like \code{fitted} to    decide how to treat the observations.}  \item{ncomp}{the number of components of the model.}  \item{method}{the method used to fit the model.  See the argument    \code{method} for possible values.}  \item{scale}{if scaling was requested (with \code{scale}), the    scaling used.}  \item{call}{the function call.}  \item{terms}{the model terms.}  \item{model}{if \code{model = TRUE}, the model frame.}  \item{x}{if \code{x = TRUE}, the model matrix.}  \item{y}{if \code{y = TRUE}, the model response.}}\references{  Martens, H., N鎠, T. (1989) \emph{Multivariate calibration.}  Chichester: Wiley.}\author{Ron Wehrens and Bj鴕n-Helge Mevik}\seealso{  \code{\link{kernelpls.fit}},  \code{\link{widekernelpls.fit}},  \code{\link{simpls.fit}},  \code{\link{oscorespls.fit}},  \code{\link{svdpc.fit}},  \code{\link{mvrCv}},  \code{\link{crossval}},  \code{\link[stats]{loadings}},  \code{\link{scores}},  \code{\link{loading.weights}},  \code{\link{coef.mvr}},  \code{\link{predict.mvr}},  \code{\link{R2}},  \code{\link{MSEP}},  \code{\link{RMSEP}},  \code{\link{plot.mvr}}}\examples{data(yarn)## Default methods:yarn.pcr <- pcr(density ~ NIR, 6, data = yarn, validation = "CV")yarn.pls <- plsr(density ~ NIR, 6, data = yarn, validation = "CV")## Alternative methods:yarn.oscorespls <- mvr(density ~ NIR, 6, data = yarn, validation = "CV",                      method = "oscorespls")yarn.simpls <- mvr(density ~ NIR, 6, data = yarn, validation = "CV",                  method = "simpls")data(oliveoil)sens.pcr <- pcr(sensory ~ chemical, ncomp = 4, scale = TRUE, data = oliveoil)sens.pls <- plsr(sensory ~ chemical, ncomp = 4, scale = TRUE, data = oliveoil)}\keyword{regression}\keyword{multivariate}