pcoa.calc: Principal Coordinates Analysis (PCoA)

In MorphoTools2: Multivariate Morphometric Analysis

Principal Coordinates Analysis (PCoA)

Description

This function performs principal coordinates analysis.

Usage

pcoa.calc(object, distMethod = "Euclidean", 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.
binaryChs, nominalChs, ordinalChs	names of categorical ordinal, categorical nominal (multistate), and binary characters. Needed for Gower's dissimilarity coefficient only, see details.

Details

The pcoa.calc function performs principal coordinates analysis using the cmdscale function from package stats. Principal coordinates analysis estimates coordinates for a set of objects in a space. Distances among objects is approximationy of the dissimilarities, based on any similarity or distance coefficient.

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 pcoadata 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).

eigenValues	eigenvalues of principal coordinates.
eigenvaluesAsPercent	eigenvalues as percent, percentage of their total sum.
cumulativePercentageOfEigenvalues	cumulative percentage of eigenvalues.
groupMeans	data.frame containing the means for the taxa.
distMethod	used distance measure.
rank	number of possitive eigenvalues.

Examples

data(centaurea)

pcoRes = pcoa.calc(centaurea, distMethod = "Manhattan")

summary(pcoRes)

plotPoints(pcoRes, 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"

pcoaGower = pcoa.calc(data, distMethod = "Gower", binaryChs = c("stemBranching"),
                      nominalChs = c("petalColour", "leaves"), ordinalChs = c("taste"))

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

MorphoTools2 documentation built on March 7, 2023, 6:18 p.m.