nmds.calc {MorphoTools2}

Non-metric Multidimensional Scaling (NMDS)

Description

This function performs Non-metric multidimensional scaling.

Usage

nmds.calc(object, distMethod = "Euclidean", k = 3, binaryChs = NULL,
                    nominalChs = NULL, ordinalChs = NULL)

Arguments

object

an object of class morphodata.

distMethod

the distance measure to be used. This must be one of: "Euclidean", "Manhattan", "Minkowski", "Jaccard", "simpleMatching", or "Gower". See details.

k

number of dimensions.

binaryChs, nominalChs, ordinalChs

names of categorical ordinal, categorical nominal (multistate), and binary characters. Needed for Gower's dissimilarity coefficient only, see details.

Details

The nmds.calc function performs non-metric multidimensional scaling using the monoMDS function from package vegan. The main threat of NMDS is, that this method doesn't preserve distances among objects in the original character space and approximates only the order of the dissimilarities among objects, based on any coefficient of similarity or distance.

Further, multiple runs of the NMDS analysis are needed to ensure that the stable ordination has been reached, as anyone run may get “trapped” in local optima which are not representative of true similarities.

The stress value reflects how well the ordination summarizes the observed relationship among the samples. A rule of thumb, 0.1-0.2 is considered fairly good, but there is no general rule since the stress is greatly influenced by the number of points. Since stress decreases as dimensionality increases, the optimal solution is when the decrease in stress is small after decreasing the number of dimensions.

Various measures of distance between the observations (rows) are applicable: (1) coefficients of distance for quantitative and binary characters: "Euclidean", "Manhattan", "Minkowski"; (2) similarity coefficients for binary characters: "Jaccard" and simple matching ("simpleMatching"); (3) coefficient for mixed data: ("Gower").

The Gower's dissimilarity coefficient can handle different types of variables. Characters have to be divided into four categories: (1) quantitative characters, (2) categorical ordinal characters, (3) categorical nominal (multistate) characters, and (4) binary characters. All characters are considered to be quantitative characters unless otherwise specified. Other types of characters have to be explicitly specified. To mark characters as ordinal, nominal, or binary, enumerate them by names using ordinalChs, nominalChs, and binaryChs arguments, respectively.

Value

an object of class nmdsdata with the following elements:

objects

	ID	IDs of each row of scores object.
	Population	population membership of each row of scores object.
	Taxon	taxon membership of each row of scores object.
	scores	ordination scores of cases (objects, OTUs).

stress

stress value, e.i., goodness of fit.

groupMeans

data.frame containing the means for the taxa.

distMethod

used distance measure.

rank

number of possitive eigenvalues.

Examples

data(centaurea)

nmdsRes = nmds.calc(centaurea, distMethod = "Euclidean", k = 3)

summary(nmdsRes)

plotPoints(nmdsRes, axes = c(1,2), col = c("red", "green", "blue", "black"),
  pch = c(20,17,8,21), pt.bg = "orange", legend = TRUE, legend.pos = "bottomright")

# using Gower's method
data = list(
    ID = as.factor(c("id1","id2","id3","id4","id5","id6")),
    Population = as.factor(c("Pop1", "Pop1", "Pop2", "Pop2", "Pop3", "Pop3")),
    Taxon = as.factor(c("TaxA", "TaxA", "TaxA", "TaxB", "TaxB", "TaxB")),
    data = data.frame(
     stemBranching = c(1, 1, 1, 0, 0, 0),  # binaryChs
     petalColour = c(1, 1, 2, 3, 3, 3),  # nominalChs; 1=white, 2=red, 3=blue
     leaves = c(1,1,1,2,2,3), # nominalChs; 1=simple, 2=palmately compound, 3=pinnately compound
     taste = c(2, 2, 2, 3, 1, 1),   # ordinal; 1=hot, 2=hotter, 3=hottest
     stemHeight = c(10, 11, 14, 22, 23, 21),         # quantitative
     leafLength = c(8, 7.1, 9.4, 1.2, 2.3, 2.1)  )   # quantitative
)
attr(data, "class") = "morphodata"

nmdsGower = nmds.calc(data, distMethod = "Gower", k = 2, binaryChs = c("stemBranching"),
                      nominalChs = c("petalColour", "leaves"), ordinalChs = c("taste"))

plotPoints(nmdsGower, axes = c(1,2), col = c("red","green"),
           pch = c(20,17), pt.bg = "orange", legend = TRUE, legend.pos = "bottomright")