vegan (version 1.8-1)

goodness.metaMDS: Goodness of Fit and Shepard Plot for Nonmetric Multidimensional Scaling

Description

Function goodness.metaMDS find goodness of fit measure for points in nonmetric multidimensional scaling, and function stressplot makes a Shepard diagram.

Usage

## S3 method for class 'metaMDS':
goodness(object, dis, ...)
stressplot(object, dis, pch, p.col = "blue", l.col = "red", lwd = 2, 
    ...)

Arguments

object

A result object from metaMDS or isoMDS.

dis

Dissimilarities. Normally this should not used with metaMDS, but should be always used with isoMDS.

pch

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

p.col, l.col

Point and line colours.

lwd

Line width.

...

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

Value

• Function goodness returns a vector of values. Function stressplot returns invisibly a Shepard object.

Details

Function 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.

Function stressplot is a wrapper to Shepard function in MASS package. It plots ordination distances against original dissimilarities, and draws a step line of the nonlinear fit. In addition, it adds to the graph two correlation like statistics on the goodness of fit. The correlation based on stress $S$ is defined as $\sqrt{1-S^2}$. The linear fit is the correlation between fitted values and ordination distances.

Both functions can be used both with metaMDS and with isoMDS. With metaMDS, the functions try to reconstruct the dissimilarities using metaMDSredist, and dissimilarities should not be given. 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.

See Also

metaMDS, isoMDS, Shepard.

Examples

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