The R Project SVN R

\name{princomp}
\alias{princomp}
\alias{plot.princomp}
\alias{print.princomp}
\alias{predict.princomp}
\alias{summary.princomp}
\alias{loadings}
\alias{screeplot}
\title{Principal Components Analysis}
\usage{
princomp(x, cor = FALSE, scores = TRUE,
         subset = rep(TRUE, nrow(as.matrix(x))))
loadings(x)
plot(x, npcs = min(10, length(x$sdev)),
          type = c("barplot", "lines"), ...) 
screeplot(x, npcs = min(10, length(x$sdev)),
          type = c("barplot", "lines"), ...) 

print(x,\dots)  summary(object)  predict(object,\dots)
}
\arguments{
  \item{x}{a matrix (or data frame) which provides the data for the
    principal components analysis.}
  \item{cor}{a logical value indicating whether the calculation should
    use the correlation matrix or the covariance matrix.}
  \item{score}{a logical value indicating whether the score on each
    principal component should be calculated.}
  \item{subset}{a vector used to select rows (observations) of the
    data matrix \code{x}.}
      
  \item{x, object}{an object of class \code{"princomp"}, as
    from \code{princomp()}.}
  \item{npcs}{the number of principal components to be plotted.}
  \item{type}{the type of plot.}
  \item{...}{graphics parameters.}
}
\description{
  \code{princomp} performs a principal components analysis on the given
  data matrix and returns the results as an object of class
  \code{princomp}.  

  \code{loadings} extracts the loadings.

  \code{screeplot} plots the variances against the number of the
  principal component. This is also the \code{plot} method.
}
\value{
  \code{princomp} returns a list with class \code{"princomp"}
  containing the following components:
  \item{sdev}{the standard deviations of the principal components
    (i.e., the square roots of the eigenvalues, rescaled by
    \code{(N-1)/N})}
  \item{loadings}{the matrix of variable loadings (i.e., a matrix
    whose columns contain the eigenvectors).}
  \item{center}{the means that were subtracted.}
  \item{scale}{the scalings applied to each variable.}
  \item{n.obs}{the number of observations.}
  \item{scores}{if \code{scores = TRUE}, the scores of the supplied
    data on the principal components.}
  \item{call}{the matched call.}
}
\details{
  The calculation is done using \code{\link{eigen}} on the correlation or
  covariance matrix, as determined by \code{\link{cor}}.  This is done for
  compatibility with the S-PLUS result (even though alternate forms for
  \code{x}---e.g., a covariance matrix---are not supported as they are
  in S-PLUS).  A preferred method of calculation is to use svd on
  \code{x}, as is done in \code{prcomp}.

  Note that the scaling of results is affected by the setting of
  \code{cor}.  If \code{cor} is \code{TRUE} then the divisor in the
  calculation of the sdev is N-1, otherwise it is N.  This has the
  effect that the result is slightly different depending on whether
  scaling is done first on the data and cor set to \code{FALSE}, or 
  done automatically in \code{princomp} with \code{cor = TRUE}.
  
  The \code{\link{print}} method for the these objects prints the
  results in a nice format and the \code{\link{plot}} method produces
  a scree plot.
}
\references{
  Mardia, K. V., J. T. Kent and J. M. Bibby (1979).
  \emph{Multivariate Analysis}, London: Academic Press.

  Venables, W. N. and B. D. Ripley (1997, 9).
  \emph{Modern Applied Statistics with S-PLUS}, Springer-Verlag.
}
\seealso{
  \code{\link{prcomp}}, \code{\link{cor}}, \code{\link{cov}},
  \code{\link{eigen}}.
}
\examples{
## the variances of the variables in the
## USArrests data vary by orders of magnitude
data(USArrests)
(pc.cr <- princomp(USArrests))
princomp(USArrests, cor = TRUE)
princomp(scale(USArrests, scale = TRUE, center = TRUE), cor = FALSE)

summary(pc.cr <- princomp(USArrests))
loadings(pc.cr)
plot(pc.cr) # does a screeplot.
biplot(pc.cr)
}
\keyword{multivariate}