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% file MASS/corresp.d
% copyright (C) 1994-2003 W. N. Venables and B. D. Ripley
%
\name{corresp}
\alias{corresp}
\alias{corresp.xtabs}
\alias{corresp.data.frame}
\alias{corresp.default}
\alias{corresp.factor}
\alias{corresp.formula}
\alias{corresp.matrix}
% \alias{biplot.correspondence}
% \alias{plot.correspondence}
% \alias{print.correspondence}
\title{
Simple Correspondence Analysis
}
\description{
Find the principal canonical correlation and corresponding row- and
column-scores from a correspondence analysis of a two-way contingency
table.
}
\usage{
corresp(x, \dots)
\method{corresp}{matrix}(x, nf = 1, \dots)
\method{corresp}{factor}(x, y, \dots)
\method{corresp}{data.frame}(x, \dots)
\method{corresp}{xtabs}(x, \dots)
\method{corresp}{formula}(formula, data, \dots)
}
\arguments{
\item{x, formula}{
The function is generic, accepting various forms of the principal
argument for specifying a two-way frequency table. Currently accepted
forms are matrices, data frames (coerced to frequency tables), objects
of class \code{"\link{xtabs}"} and formulae of the form \code{~ F1 + F2},
where \code{F1} and \code{F2} are factors.
}
\item{nf}{
The number of factors to be computed. Note that although 1 is the most
usual, one school of thought takes the first two singular vectors for
a sort of biplot.
}
\item{y}{a second factor for a cross-classification}
\item{data}{a data frame against which to preferentially resolve
variables in the formula.}
\item{\dots}{
If the principal argument is a formula, a data frame may be specified
as well from which variables in the formula are preferentially
satisfied.
}}
\value{
An list object of class \code{"correspondence"} for which
\code{print}, \code{plot} and \code{biplot} methods are supplied.
The main components are the canonical correlation(s) and the row
and column scores.
}
\details{
See Venables \& Ripley (2002). The \code{plot} method produces a graphical
representation of the table if \code{nf=1}, with the \emph{areas} of circles
representing the numbers of points. If \code{nf} is two or more the
\code{biplot} method is called, which plots the second and third columns of
the matrices \code{A = Dr^(-1/2) U L} and \code{B = Dc^(-1/2) V L} where the
singular value decomposition is \code{U L V}. Thus the x-axis is the
canonical correlation times the row and column scores. Although this
is called a biplot, it does \emph{not} have any useful inner product
relationship between the row and column scores. Think of this as an
equally-scaled plot with two unrelated sets of labels. The origin is
marked on the plot with a cross. (For other versions of this plot see
the book.)
}
\references{
Venables, W. N. and Ripley, B. D. (2002)
\emph{Modern Applied Statistics with S.} Fourth edition. Springer.
Gower, J. C. and Hand, D. J. (1996)
\emph{Biplots.} Chapman \& Hall.
}
\seealso{
\code{\link{svd}}, \code{\link{princomp}}
}
\examples{
(ct <- corresp(~ Age + Eth, data = quine))
\dontrun{plot(ct)}
corresp(caith)
biplot(corresp(caith, nf = 2))
}
\keyword{category}
\keyword{multivariate}
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