Morpho (version 2.1)

groupPCA: Perform PCA based of the group means' covariance matrix

Description

Calculate covariance matrix of the groupmeans and project all observations into the eigenspace of this covariance matrix. This displays a low dimensional between group structure of a high dimensional problem.

Usage

groupPCA(dataarray, groups, rounds = 10000, tol = 1e-10, cv = TRUE,
  mc.cores = parallel::detectCores(), weighting = TRUE)

Arguments

dataarray

Either a k x m x n real array, where k is the number of points, m is the number of dimensions, and n is the sample size. Or alternatively a n x m Matrix where n is the numeber of observations and m the number of variables (this can be PC scores for exampl

groups

a character/factor vector containgin grouping variable.

rounds

integer: number of permutations if a permutation test of the euclidean distance between group means is requested.If rounds = 0, no test is performed.

tol

threshold to ignore eigenvalues of the covariance matrix.

cv

logical: requests leaving-one-out crossvalidation

mc.cores

integer: how many cores of the Computer are allowed to be used. Default is use autodetection by using detectCores() from the parallel package. Parallel processing is disabled on Windows due to occasional errors.

weighting

logical:weight between groups covariance matrix according to group sizes.

Value

• eigenvalues
  Non-zero eigenvalues of the groupmean covariance matrix
• groupPCs
  PC-axes - i.e. eigenvectors of the groupmean covariance matrix
• Variance
  table displaying the variance explained by eache eigenvalue
• Scores
  Scores of all observation in the PC-space
• probs
  p-values of pairwise groupdifferences - based on permuation testing
• groupdists
  Euclidean distances between groups' averages
• groupmeans
  Groupmeans
• Grandmean
  Grand mean
• CV
  Cross-validated scores
• groups
  grouping Variable

References

Mitteroecker P, Bookstein F 2011. Linear Discrimination, Ordination, and the Visualization of Selection Gradients in Modern Morphometrics. Evolutionary Biology 38:100-114.

Boulesteix, A. L. 2005: A note on between-group PCA, International Journal of Pure and Applied Mathematics 19, 359-366.

See Also

CVA

Examples

require(car)
data(iris)
vari <- iris[,1:4]
facto <- iris[,5]
pca.1 <-groupPCA(vari,groups=facto,rounds=100,mc.cores=1)

### plot scores
scatterplotMatrix(pca.1$Scores,groups=facto, ellipse=TRUE,
        by.groups=TRUE,var.labels=c("PC1","PC2","PC3"))

## example with shape data
data(boneData)
proc <- procSym(boneLM)
pop_sex <- name2factor(boneLM, which=3:4)
gpca <- groupPCA(proc$orpdata, groups=pop_sex, rounds=0, mc.cores=2)
## visualize shape associated with first between group PC
dims <- dim(proc$mshape)
## calculate matrix containing landmarks of grandmean
grandmean <- matrix(gpca$Grandmean, dims[1], dims[2])
## calculate landmarks from first between-group PC
#                   (+2 and -2 standard deviations)
gpcavis2sd<- showPC(2*sd(gpca$Scores[,1]), gpca$groupPCs, grandmean)
gpcavis2sd.neg<- showPC(-2*sd(gpca$Scores[,1]), gpca$groupPCs, grandmean)
deformGrid3d(gpcavis2sd, gpcavis2sd.neg, ngrid = 0)
require(rgl)
## visualize grandmean mesh

grandm.mesh <- warp.mesh(skull_0144_ch_fe.mesh, boneLM[,,1],grandmean)
wire3d(grandm.mesh, col="white")
spheres3d(grandmean, radius=0.005)