PrincipalCoordinates {MultBiplotR}

Principal Coordinates Analysis

Description

Principal coordinates Analysis for a matrix of proximities obtained from binary, categorical, continuous or mixed data

Usage

PrincipalCoordinates(Proximities, w = NULL, dimension = 2, 
method = "eigen", tolerance = 1e-04, Bootstrap = FALSE, 
BootstrapType = c("Distances", "Products"), nB = 200, 
ProcrustesRot = TRUE, BootstrapMethod = c("Sampling", "Permutation"))

Arguments

Proximities

An object of class proximities.

w

An set of weights.

dimension

Dimension of the solution

method

Method to calculate the eigenvalues and eigenvectors. The default is the usual eigen function although the Power Method to calculate only tre first eigenvectors can be used.

tolerance

Tolerance for the eigenvalues

Bootstrap

Should Bootstrap be calculated?

BootstrapType

Bootstrap on the residuals of the "distance" or "scalar products" matrix.

nB

Number of Bootstrap replications

ProcrustesRot

Should each replication be rotated to match the initial solution?

BootstrapMethod

The replications are obtained "Sampling" or "Permutating" the residuals.

Details

Principal Coordinates Analysis for a proximity matrix previously calculated from a matrix of raw data or directly obsrved proximities.

Value

An object of class Principal.Coordinates. The function adds the information of the Principal Coordinates to the object of class proximities. Together with the information about the proximities the object has:

Analysis

The type of analysis performed, "Principal Coordinates" in this case

Eigenvalues

The eigenvalues of the PCoA

Inertia

The Inertia of the PCoA

RowCoordinates

Coordinates for the objects in the PCoA

RowQualities

Qualities of representation for the objects in the PCoA

RawStress

Raw Stress values

stress1

stress formula 1

stress2

stress formula 2

sstress1

sstress formula 1

sstress2

sstress formula 2

rsq

Squared correlation between disparities and distances

Spearman

Spearman correlation between disparities and distances

Kendall

Kendall correlation between disparities and distances

BootstrapInfo

The result of the bootstrap calculations

Author(s)

Jose Luis Vicente-Villardon

References

Gower, J. C. (2006) Similarity dissimilarity and Distance, measures of. Encyclopedia of Statistical Sciences. 2nd. ed. Volume 12. Wiley

Gower, J.C. (1966). Some distance properties of latent root and vector methods used in multivariate analysis. Biometrika 53: 325-338.

J.R. Demey, J.L. Vicente-Villardon, M.P. Galindo, A.Y. Zambrano, Identifying molecular markers associated with classifications of genotypes by external logistic biplot, Bioinformatics 24 (2008) 2832.

See Also

BinaryProximities, BootstrapDistance, BootstrapDistance, BinaryProximities

Examples

data(spiders)
Dis=BinaryProximities(spiders)
pco=PrincipalCoordinates(Dis)
Dis=BinaryProximities(spiders)
pco=PrincipalCoordinates(Dis, Bootstrap=TRUE)