wcmdscale {vegan} | R Documentation |

Weighted classical multidimensional scaling,
also known as weighted *principal coordinates analysis*.

wcmdscale(d, k, eig = FALSE, add = FALSE, x.ret = FALSE, w)

`d` |
a distance structure such as that returned by `dist`
or a full symmetric matrix containing the dissimilarities. |

`k` |
the dimension of the space which the data are to be
represented in; must be in {1,2,...,n-1}. If missing,
all dimensions with above zero eigenvalue. |

`eig` |
indicates whether eigenvalues should be returned. |

`add` |
logical indicating if an additive constant c* should
be computed, and added to the non-diagonal dissimilarities such that
all n-1 eigenvalues are non-negative. Not implemented. |

`x.ret` |
indicates whether the doubly centred symmetric distance matrix should be returned. |

`w` |
Weights of points. |

Function `wcmdscale`

is based on function
`cmdscale`

(package stats of base **R**), but it uses
point weights. Points with high weights will have a stronger
influence on the result than those with low weights. Setting equal
weights `w = 1`

will give ordinary multidimensional scaling.

If `eig = FALSE`

and `x.ret = FALSE`

(default), a matrix
with `k`

columns whose rows give the coordinates of the points
chosen to represent the dissimilarities.

Otherwise, an object of class `wcmdscale`

list containing the
following components.

`points` |
a matrix with `k` columns whose rows give the
coordinates of the points chosen to represent the dissimilarities. |

`eig` |
the n-1 eigenvalues computed during the scaling process if
`eig` is true. |

`x` |
the doubly centred and weighted distance matrix if `x.ret` is true. |

`weights` |
Weights. |

`negaxes` |
A matrix of scores for axes with negative eigenvalues scaled
by the absolute eigenvalues similarly as `points` . This is `NULL`
if there are no negative eigenvalues or `k` was specified, and would not include negative eigenvalues. |

Gower, J. C. (1966)
Some distance properties of latent root and vector
methods used in multivariate analysis.
*Biometrika* **53**, 325–328.

Mardia, K. V., Kent, J. T. and Bibby, J. M. (1979). Chapter 14 of
*Multivariate Analysis*, London: Academic Press.

`cmdscale`

.
Also `isoMDS`

and `sammon`

in package MASS.

## Correspondence analysis as a weighted principal coordinates ## analysis of Euclidean distances of Chi-square transformed data data(dune) rs <- rowSums(dune)/sum(dune) d <- dist(decostand(dune, "chi")) ord <- wcmdscale(d, w = rs, eig = TRUE) ## Ordinary CA ca <- cca(dune) ## Eigevalues are numerically similar ca$CA$eig - ord$eig ## Configurations are similar when site scores are scaled by ## eigenvalues in CA procrustes(ord, ca, choices=1:19, scaling = 1) plot(procrustes(ord, ca, choices=1:2, scaling=1)) ## Reconstruction of non-Euclidean distances with negative eigenvalues d <- vegdist(dune) ord <- wcmdscale(d, eig = TRUE) ## Only positive eigenvalues: cor(d, dist(ord$points)) ## Correction with negative eigenvalues: cor(d, sqrt(dist(ord$points)^2 - dist(ord$negaxes)^2))

[Package *vegan* version 1.16-32 Index]