vegan (version 2.6-6.1)

# stressplot.wcmdscale: 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`, `dbrda`, `prcomp` and `princomp`.

## Usage

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

## Value

Functions draw a graph and return invisibly the ordination distances or the ordination distances.

## Arguments

object

Result object from eigenvector ordination (`wcmdscale`, `rda`, `cca`, `dbrda`, `capscale`)

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 `stressplot`

...

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

Jari Oksanen.

## 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-Euclidean distances (in `wcmdscale`, `dbrda` 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 `dbrda`, `capscale` or `wcmdscale` with argument `add` to avoid negative eigenvalues, the ordination distances will exceed the observed dissimilarities.

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. The exception is `dbrda` where the distances in partial, constrained and residual components are not additive, and only the first of these components can be shown, and partial models cannot be shown at all.

`stressplot` and `stressplot.monoMDS` for standard Shepard diagrams.

## Examples

Run this code
``````data(dune, dune.env)
mod <- rda(dune)
stressplot(mod)
mod <- rda(dune ~ Management, dune.env)
stressplot(mod, k=3)
``````

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