Multidimensional scaling or principal coordinates analysis

Perform a PCoA (`type = "metric"). or other forms of MDS.

mds(
  dist,
  k = 2,
  type = c("metric", "nonmetric", "cmdscale", "wcmdscale", "sammon", "isoMDS", "monoMDS",
    "metaMDS"),
  p = 2,
  ...
)

# S3 method for class 'mds'
plot(x, y, ...)

# S3 method for class 'mds'
autoplot(object, labels, col, ...)

# S3 method for class 'mds'
chart(data, labels, col, ..., type = NULL, env = parent.frame())

shepard(dist, mds, p = 2)

# S3 method for class 'shepard'
plot(
  x,
  y,
  l.col = "red",
  l.lwd = 1,
  xlab = "Observed Dissimilarity",
  ylab = "Ordination Distance",
  ...
)

# S3 method for class 'shepard'
autoplot(
  object,
  alpha = 0.5,
  l.col = "red",
  l.lwd = 1,
  xlab = "Observed Dissimilarity",
  ylab = "Ordination Distance",
  ...
)

# S3 method for class 'shepard'
chart(
  data,
  alpha = 0.5,
  l.col = "red",
  l.lwd = 1,
  xlab = "Observed Dissimilarity",
  ylab = "Ordination Distance",
  ...,
  type = NULL,
  env = parent.frame()
)

# S3 method for class 'mds'
augment(x, data, ...)

# S3 method for class 'mds'
glance(x, ...)

Arguments

dist: A dist object from stats::dist() or other compatible functions like vegan::vegdist(), or a Dissimilarity object, see dissimilarity().
k: The dimensions of the space for the representation, usually k = 2 (by default). It should be possible to use also k = 3 with extra care and custom plots.
type: Not used
p: For types "nonmetric", "metaMDS", "isoMDS", "monoMDS" and "sammon", a Shepard plot is also precalculated. pis the power for Minkowski distance in the configuration scale. By default, p = 2. Leave it like that if you don't understand what it means see MASS::Shepard().
...: More arguments (see respective types or functions)
x: Idem
y: Not used
object: An mds object
labels: Points labels on the plot (optional)
col: Points color (optional)
data: A data frame to augment with columns from the MDS analysis
env: Not used
mds: Idem
l.col: Color of the line in the Shepard's plot (red by default)
l.lwd: Width of the line in the Shepard"s plot (1 by default)
xlab: Label for the X axis (a default value exists)
ylab: Idem for the Y axis
alpha: Alpha transparency for points (0.5 by default, meaning 50% transparency)

Value

A mds object, which is a list containing all components from the corresponding function, plus possibly Shepard if the Shepard plot is precalculated.

Examples

library(chart)
data(iris, package = "datasets")
iris_num <- iris[, -5] # Only numeric columns
iris_dis <- dissimilarity(iris_num, method = "euclidean")

# Metric MDS
iris_mds <- mds$metric(iris_dis)
chart(iris_mds, labels = 1:nrow(iris), col = iris$Species)
#> Warning: ggrepel: 126 unlabeled data points (too many overlaps). Consider increasing max.overlaps


# Non-metric MDS
iris_nmds <- mds$nonmetric(iris_dis)
#> Run 0 stress 0.02525035 
#> Run 1 stress 0.03821335 
#> Run 2 stress 0.0307977 
#> Run 3 stress 0.02525036 
#> ... Procrustes: rmse 0.0001001939  max resid 0.0006323391 
#> ... Similar to previous best
#> Run 4 stress 0.03567161 
#> Run 5 stress 0.03182264 
#> Run 6 stress 0.03104432 
#> Run 7 stress 0.03102056 
#> Run 8 stress 0.02525023 
#> ... New best solution
#> ... Procrustes: rmse 7.201641e-05  max resid 0.0004834757 
#> ... Similar to previous best
#> Run 9 stress 0.04026037 
#> Run 10 stress 0.02525391 
#> ... Procrustes: rmse 0.0004747481  max resid 0.003622262 
#> ... Similar to previous best
#> Run 11 stress 0.04677425 
#> Run 12 stress 0.03079765 
#> Run 13 stress 0.0310176 
#> Run 14 stress 0.04210446 
#> Run 15 stress 0.04134393 
#> Run 16 stress 0.04408108 
#> Run 17 stress 0.02525033 
#> ... Procrustes: rmse 7.163061e-05  max resid 0.0004469441 
#> ... Similar to previous best
#> Run 18 stress 0.04804817 
#> Run 19 stress 0.04076145 
#> Run 20 stress 0.02528288 
#> ... Procrustes: rmse 0.001629791  max resid 0.01659899 
#> *** Best solution repeated 3 times
chart(iris_nmds, labels = 1:nrow(iris), col = iris$Species)
#> Warning: ggrepel: 126 unlabeled data points (too many overlaps). Consider increasing max.overlaps

glance(iris_nmds) # Good R^2
#> # A tibble: 1 × 2
#>   linear_R2 nonmetric_R2
#>       <dbl>        <dbl>
#> 1     0.998        0.999
iris_sh <- shepard(iris_dis, iris_nmds)
chart(iris_sh) # Excellent matching + linear -> metric MDS is OK here