screeplot_NMDS: Scree plot/Stress plot for NMDS

In fgoral/goeveg: Functions for Community Data and Ordinations

Scree plot/Stress plot for NMDS

Description

This function provides a plot of stress values against a given number of tested dimensions (default k = 6) in NMDS. This scree plot (or stress plot) shows the decrease in ordination stress with an increase in the number of ordination dimensions. It is based on function metaMDS (vegan package) and uses the monoMDS engine.

Usage

screeplot_NMDS(
  matrix,
  distance = "bray",
  k = 6,
  trymax = 20,
  autotransform = TRUE
)

Arguments

matrix	Community data, a matrix-like object with samples in rows and species in columns.
distance	Dissimilarity index used in vegdist.
k	Number of dimensions (default k = 6).
trymax	Maximum number of random configuration for iterative search search of stable solution.
autotransform	Whether to use transformation (see metaMDS) or not. Default is autotransform = TRUE.

Value

A numeric vector of length k containing stress values for k dimensions.

Details

The simplest indicator for the goodness of non-metric multidimensional scaling (NMDS) is the stress value. Stress is a value between 0 and 1 and expresses a proportion between the distance in the original dissimilarity matrix and the fitted distance in ordination space. The lower the stress value, the better is the fit. Details and exact formula are found under function monoMDS. Stress value depends on dimensionality: it is decreasing with increasing dimensionality. On the other hand, stress-reduction does not mean to maximize interpretation capability. Low-dimensional projections are often better to interpret and are so preferable for interpretation issues.

A scree plot (or sometimes also called stress plot) is a diagnostic plot to explore both, dimensionality and interpretative value. Often the 'elbow' of the plot is an indicator to determine the optimal number of dimensions to capture most information contained in the data. However, for ecological data this is rarely seen, so that the following rule of thumb under consideration of the interpretability can be used.

Clarke 1993 suggests the following guidelines for stress values: <0.05 = excellent, <0.10 = good, <0.20 = usable without putting too much reliance on details, >0.20 = could be dangerous to interpret, > 0.35 = samples effectively randomly placed. The plot shows the border of the 0.20 stress value limit. Solutions with higher stress values should be interpreted with caution and those with stress above 0.35 are highly suspect.

It should be taken into account that the stress value naturally increases with the number of samples and/or variables: “The greater the number of samples, the harder it will be to reflect the complexity of their inter-relationship in a two-dimensional plot” (Clarke 1993, p. 125). Furthermore high stress values can be attributed to all points or only to few or even single points, that represent samples different to the others.

The scree plot is not an exclusive method to determine the optimal number of dimensions. The effect of individual points on the stress value can be explored with the goodness-function. Large values indicate poor fit and can be easily visualized in an ordination diagram.

Another diagnostic plot is the the Shepard diagram (stressplot), which is a scatterplot of the (Euclidean) distances in ordination space against the original dissimilarities. However, as the number of pairwise elements increases rapidly with the number of samples, the Shepard diagram will mostly lead to a high ‘correlation-like' fit and lacks therefore a reliable and precise interpretability.

Author(s)

Friedemann von Lampe ([e-mail]) and Jenny Schellenberg

References

Clarke, K. R. (1993). Non-parametric multivariate analysis of changes in community structure. Austral J Ecol 18: 117-143. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/j.1442-9993.1993.tb00438.x")}

See Also

metaMDS stressplot

Examples

## Use of function with default values
screeplot_NMDS(schedenveg)

## Use of function for testing 10 dimensions
screeplot_NMDS(schedenveg, k = 10)

## Alternative diagnostic plots
library(vegan)
nmds <- metaMDS(schedenveg, k = 2)

# Draw Shepard plot
stressplot(nmds)

# Calculate goodness of fit
gof <- goodness(object = nmds)

# Draw NMDS ordination diagram with sites
plot(nmds, display = "sites", type = "n", cex = 0.7)
# Add the points with size reflecting goodness of fit (bigger = worse fit)
points(nmds, display = "sites", cex = 2*gof/mean(gof))

fgoral/goeveg documentation built on Feb. 27, 2024, 6:32 a.m.