Morpho (version 1.0-1)

covDist: calculate distances and PC-coordinates of covariance matrices

Description

calculate PC-coordinates of covariance matrices by using the Riemannian metric in their respective space.

Usage

covDist(s1, s2)
covPCA(data, groups, scores=TRUE, rounds=0, mc.cores=detectCores())

Arguments

s1

m x m covariance matrix

s2

m x m covariance matrix

data

matrix containing data with one row per observation.

groups

factor: group assignment for each specimen.

scores

logical: PCscores are calculated from distance matrix.

rounds

integer: rounds to run permutation of distances by randomly assigning group membership.

mc.cores

integer: how many CPU-cores shall be used in permutation testing (not available on Windows)

Value

• covDist returns the distance between s1 and s2, while covPCA returns a list containing:
• dist
  distance matrix
• if scores = TRUE
• PCscores
  PCscores
• eigen
  eigen decomposition of the centered inner product
• if rounds > 0
• p.matrix
  p-values for pairwise distances from permutation testing

Details

covDist calculates the Distance between covariance matrices. And covPCA uses a MDS (multidimensional scaling) approach to obtain PC-coordinates from a distance matrix derived from multiple groups. P-values for pairwise distances can be computed by permuting group membership and comparing actual distances to those obtained from random resampling.

References

Mitteroecker P, Bookstein F. 2009. The ontogenetic trajectory of the phenotypic covariance matrix, with examples from craniofacial shape in rats and humans. Evolution 63:727-737.

Hastie T, Tibshirani R, Friedman JJH. 2013. The elements of statistical learning. Springer New York.

See Also

prcomp

Examples

require(car)
cpca <- covPCA(iris[,1:4],iris[,5])
sp(cpca$PCscores[,1],cpca$PCscores[,2],groups=levels(iris[,5]),
   smooth=FALSE,xlim=range(cpca$PCscores),ylim=range(cpca$PCscores))

data(boneData)
proc <- procSym(boneLM)
pop <- name2factor(boneLM, which=3)
## compare covariance matrices for PCscores of Procrustes fitted data
cpca1 <- covPCA(proc$PCscores, groups=pop, rounds = 100, mc.cores=2)
## view p-values:
cpca1$p.matrix # differences between covariance matrices
# are significant
## visualize covariance ellipses of first 5 PCs of shape
spm(proc$PCscores[,1:5], groups=pop, smooth=FALSE,ellipse=TRUE, by.groups=TRUE)
## covariance seems to differ between 1st and 5th PC
## for demonstration purposes, try only first 4 PCs
cpca2 <- covPCA(proc$PCscores[,1:4], groups=pop, rounds = 100,
mc.cores=2)
## view p-values:
cpca2$p.matrix # significance is gone