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

In Morpho: Calculations and Visualisations Related to Geometric Morphometrics

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 example)
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 between-group variance explained by each between group PC - this only reflects the variability of the group means and NOT the variability of the data projected into that space
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	matrix with rows containing the Groupmeans, or a k x m x groupsize array if the input is a k x m x n landmark array
Grandmean	vector containing the Grand mean, or a matrix if the input is a k x m x n landmark array
CV	Cross-validated scores
groups	grouping Variable
resPCs	PCs orthogonal to the between-group PCs
resPCscores	Scores of the residualPCs
resVar	table displaying the residual variance explained by each residual PC.

Author(s)

Stefan Schlager

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

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

### plot scores
if (require(car)) {
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)
## Not run: 
## visualize shape associated with first between group PC
dims <- dim(proc$mshape)
## calculate matrix containing landmarks of grandmean
grandmean <-gpca$Grandmean
## calculate landmarks from first between-group PC
#                   (+2 and -2 standard deviations)
gpcavis2sd<- restoreShapes(c(-2,2)*sd(gpca$Scores[,1]), gpca$groupPCs[,1], grandmean)
deformGrid3d(gpcavis2sd[,,1], gpcavis2sd[,,2], ngrid = 0,size=0.01)
require(rgl)
## visualize grandmean mesh

grandm.mesh <- tps3d(skull_0144_ch_fe.mesh, boneLM[,,1],grandmean,threads=1)
wire3d(grandm.mesh, col="white")
spheres3d(grandmean, radius=0.01)

## End(Not run)

Morpho documentation built on Feb. 16, 2023, 10:51 p.m.