# 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
(`stressplot`

for non-metric multidimensional scaling
with `metaMDS`

or `monoMDS`

), but shows the
linear relationship of the eigenvector ordinations. The
`stressplot`

methods are available for `wcmdscale`

,
`rda`

, `cca`

, `capscale`

,
`prcomp`

and `princomp`

.

### Usage

1 2 3 | ```
## S3 method for class 'wcmdscale'
stressplot(object, k = 2, pch, p.col = "blue", l.col = "red",
lwd = 2, ...)
``` |

### Arguments

`object` |
Result object from eigenvector ordination ( |

`k` |
Number of dimensions for which the ordination distances are displayed. |

`pch, p.col, l.col, lwd` |
Plotting character, point colour and line colour like in
default |

`...` |
Other parameters to functions, e.g. graphical parameters. |

### Details

The functions offer a similar display for eigenvector
ordinations as the standard Shepard diagram (`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-metric distances (in
`wcmdscale`

or `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
`capscale`

with argument `add = TRUE`

to avoid
negative eigenvalues, the ordination distances will exceed the
observed dissimilarities by the additive constant.

In partial ordination (`cca`

, `rda`

and
`capscale`

with `Condition`

in the formula), the
distances in the partial component are included both in the observed
distances and in ordination distances. With `k=0`

, the
ordination distances refer to the partial ordination.

### Value

Functions draw a graph and return invisibly the ordination distances.

### Author(s)

Jari Oksanen.

### See Also

`stressplot`

and `stressplot.monoMDS`

for
standard Shepard diagrams.

### Examples

1 2 3 4 5 | ```
data(dune, dune.env)
mod <- rda(dune)
stressplot(mod)
mod <- rda(dune ~ Management, dune.env)
stressplot(mod, k=3)
``` |

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