`goodness.metaMDS`

find goodness of fit measure for
points in nonmetric multidimensional scaling, and function
`stressplot`

makes a `Shepard`

diagram.
```
"goodness"(object, dis, ...)
"stressplot"(object, dis, pch, p.col = "blue", l.col = "red", lwd = 2, ...)
```

pch

Plotting character for points. Default is dependent on the
number of points.

p.col, l.col

Point and line colours.

lwd

Line width. For

`monoMDS`

the default is
`lwd = 1`

if more than two lines are drawn, and `lwd = 2`

otherwise....

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

`goodness`

returns a vector of values. Function
`stressplot`

returns invisibly an object with items for
original dissimilarities, ordination distances and fitted values. `goodness.metaMDS`

finds a goodness of fit statistic
for observations (points). This is defined so that sum of squared
values is equal to squared stress. Large values indicate poor fit.
The absolute values of the goodness statistic depend on the
definition of the stress: `isoMDS`

expresses
stress in percents, and therefore its goodness values are 100 times
higher than those of `monoMDS`

which expresses the
stress as a proportion. Function `stressplot`

draws a Shepard diagram which is a plot
of ordination distances and monotone or linear fit line against
original dissimilarities. In addition, it displays two
correlation-like statistics on the goodness of fit in the graph.
The nonmetric fit is based on stress $S$ and defined as $R2 = 1-S*S$. The “linear fit” is the squared
correlation between fitted values and ordination distances. For
`monoMDS`

, the “linear fit” and $R2$
from “stress type 2” are equal.

Both functions can be used with `metaMDS`

,
`monoMDS`

and `isoMDS`

. The original
dissimilarities should not be given for `monoMDS`

or
`metaMDS`

results (the latter tries to reconstruct the
dissimilarities using `metaMDSredist`

if
`isoMDS`

was used as its engine). With
`isoMDS`

the dissimilarities must be given. In
either case, the functions inspect that dissimilarities are
consistent with current ordination, and refuse to analyse
inconsistent dissimilarities. Function `goodness.metaMDS`

is
generic in vegan, but you must spell its name completely with
`isoMDS`

which has no class.

`metaMDS`

, `monoMDS`

,
`isoMDS`

, `Shepard`

. Similar
diagrams for eigenvector ordinations can be drawn with
`stressplot.wcmdscale`

, `stressplot.cca`

,
`stressplot.rda`

and `stressplot.capscale`

.
```
data(varespec)
mod <- metaMDS(varespec)
stressplot(mod)
gof <- goodness(mod)
gof
plot(mod, display = "sites", type = "n")
points(mod, display = "sites", cex = 2*gof/mean(gof))
```

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