PrincipalCoordinates function

Principal Coordinates Analysis

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

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.

Returns

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

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.

Author(s)

Jose Luis Vicente-Villardon

See Also

BinaryProximities, BootstrapDistance, BootstrapDistance, BinaryProximities

Examples

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