\name{stressplot.wcmdscale}
\alias{stressplot.wcmdscale}
\alias{stressplot.cca}
\alias{stressplot.rda}
\alias{stressplot.capscale}
\alias{stressplot.dbrda}
\alias{stressplot.prcomp}
\alias{stressplot.princomp}

\title{
  Display Ordination Distances Against Observed Distances in Eigenvector Ordinations
}

\description{
  Functions plot ordination distances in given number of dimensions
  against observed distances or distances in full space in eigenvector
  methods. The display is similar as the Shepard diagram
  (\code{\link{stressplot}} for non-metric multidimensional scaling
  with \code{\link{metaMDS}} or \code{\link{monoMDS}}), but shows the
  linear relationship of the eigenvector ordinations. The
  \code{stressplot} methods are available for \code{\link{wcmdscale}},
  \code{\link{rda}}, \code{\link{cca}}, \code{\link{capscale}},
  \code{\link{dbrda}}, \code{\link{prcomp}} and \code{\link{princomp}}. 
}

\usage{
\method{stressplot}{wcmdscale}(object, k = 2, pch, p.col = "blue", l.col = "red",
    lwd = 2, ...)
}

\arguments{
  \item{object}{
    Result object from eigenvector ordination (\code{\link{wcmdscale}},
    \code{\link{rda}}, \code{\link{cca}}, \code{\link{capscale}})
}
  \item{k}{
    Number of dimensions for which the ordination distances are displayed.
}
  \item{pch, p.col, l.col, lwd}{
    Plotting character, point colour and line colour like in
    default \code{\link{stressplot}}
}
  \item{\dots}{
    Other parameters to functions, e.g. graphical parameters.
}
}

\details{ The functions offer a similar display for eigenvector
  ordinations as the standard Shepard diagram (\code{\link{stressplot}})
  in non-metric multidimensional scaling. The ordination distances in
  given number of dimensions are plotted against observed
  distances. With metric distances, the ordination distances in full
  space (with all ordination axes) are equal to observed distances, and
  the fit line shows this equality. In general, the fit line does not go
  through the points, but the points for observed distances approach the
  fit line from below. However, with non-Euclidean distances (in
  \code{\link{wcmdscale}} or \code{\link{capscale}}) with negative
  eigenvalues the ordination distances can exceed the observed distances
  in real dimensions; the imaginary dimensions with negative eigenvalues
  will correct these excess distances. If you have used
  \code{\link{capscale}} or \code{\link{wcmdscale}} with argument
  \code{add} to avoid negative eigenvalues, the ordination distances
  will exceed the observed dissimilarities.

  In partial ordination (\code{\link{cca}}, \code{\link{rda}} and
  \code{\link{capscale}} with \code{Condition} in the formula), the
  distances in the partial component are included both in the observed
  distances and in ordination distances.  With \code{k=0}, the
  ordination distances refer to the partial ordination.

}

\value{
  Functions draw a graph and return invisibly the ordination distances
  or the ordination distances.
}

\author{
  Jari Oksanen.
}

\seealso{
  \code{\link{stressplot}} and \code{\link{stressplot.monoMDS}} for
  standard Shepard diagrams.
}

\examples{
data(dune, dune.env)
mod <- rda(dune)
stressplot(mod)
mod <- rda(dune ~ Management, dune.env)
stressplot(mod, k=3)
}

\keyword{ multivariate }

