covDist: calculates distances and PC-coordinates of covariance...

In Morpho: Calculations and Visualisations Related to Geometric Morphometrics

calculates distances and PC-coordinates of covariance matrices

Description

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

Usage

covDist(s1, s2)

covPCA(
  data,
  groups,
  rounds = 1000,
  bootrounds = 0,
  lower.bound = 0.05,
  upper.bound = 0.95
)

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
rounds	integer: rounds to run permutation of distances by randomly assigning group membership
bootrounds	integer: perform bootstrapping to generate confidence intervals (lower boundary, median and upper boundary) for PC-scores.
lower.bound	numeric: set probability (quantile) for lower boundary estimate from bootstrapping.
upper.bound	numeric: set probability (quantile) for upper boundary estimate from bootstrapping.

Details

covDist calculates the Distance between covariance matrices while 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. To calculate confidence intervals for PC-scores, within-group bootstrapping can be performed.

Value

covDist returns the distance between s1 and s2

covPCA returns a list containing:

if scores = TRUE

PCscores	PCscores
eigen	eigen decomposition of the centered inner product

if rounds > 0

dist	distance matrix
p.matrix	p-values for pairwise distances from permutation testing

if bootrounds > 0

bootstrap	list containing the lower and upper bound of the confidence intervals of PC-scores as well as the median of bootstrapped values.
boot.data	array containing all results generated from bootstrapping.

Author(s)

Stefan Schlager

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

cpca <- covPCA(iris[,1:4],iris[,5])
cpca$p.matrix #show pairwise p-values for equal covariance matrices
## Not run: 
require(car)
sp(cpca$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$PCscores, groups=pop, rounds = 1000)
## view p-values:
cpca1$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 = 1000)
## view p-values:
cpca2$p.matrix # significance is gone

## End(Not run)

#do some bootstrapping 1000 rounds
cpca <- covPCA(iris[,1:4],iris[,5],rounds=0, bootrounds=1000)
#plot bootstrapped data of PC1 and PC2 for first group
plot(t(cpca$boot.data[1,1:2,]),xlim=range(cpca$boot.data[,1,]),
                               ylim=range(cpca$boot.data[,2,]))
points(t(cpca$PCscores[1,]),col="white",pch=8,cex=1.5)##plot actual values
                      
for (i in 2:3) {
  points(t(cpca$boot.data[i,1:2,]),col=i)##plot other groups
  points(t(cpca$PCscores[i,]),col=1,pch=8,cex=1.5)##plot actual values
}

Morpho documentation built on June 22, 2024, 7:19 p.m.