phyl.pca_pl {RPANDA}

Regularized Phylogenetic Principal Component Analysis (PCA).

Description

Performs a principal component analysis (PCA) on a regularized evolutionary variance-covariance matrix obtained using the fit_t_pl function.

Usage

phyl.pca_pl(object, plot=TRUE, ...)
  

Arguments

object

A penalized likelihood model fit obtained by the fit_t_pl function.

plot

Plot of the PC's axes. Default is TRUE (see details).'

...

Options to be passed through. (e.g., axes=c(1,2), col, pch, cex, mode="cov" or "corr", etc.)

Details

phyl.pca_pl allows computing a phylogenetic principal component analysis (following Revell 2009) using a regularized evolutionary variance-covariance matrix from penalized likelihood models fit to high-dimensional datasets (where the number of variables p is potentially larger than n; see details for the models options in fit_t_pl). Models estimates are more accurate than maximum likelihood methods, particularly in the high-dimensional case. Ploting options, the number of axes to display (axes=c(1,2) is the default), and whether the covariance (mode="cov") or correlation (mode="corr") should be used can be specified through the ellipsis "..." argument.

Value

a list with the following components

values

the eigenvalues of the evolutionary variance-covariance matrix

scores

the PC scores

loadings

the component loadings

nodes_scores

the scores for the ancestral states at the nodes (projected on the space of the tips)

mean

the mean/ancestral value used to center the data

vectors

the eigenvectors of the evolutionary variance-covariance matrix

Note

Contrary to conventional PCA, the principal axes of the phylogenetic PCA are not orthogonal, they represent the main axes of (independent) evolutionary changes.

Author(s)

J. Clavel

References

Revell, L.J., 2009. Size-correction and principal components for intraspecific comparative studies. Evolution, 63:3258-3268.

Clavel, J., Aristide, L., Morlon, H., 2019. A Penalized Likelihood framework for high-dimensional phylogenetic comparative methods and an application to new-world monkeys brain evolution. Syst. Biol. 68: 93-116.

See Also

fit_t_pl, ancestral, GIC.fit_pl.rpanda, gic_criterion

Examples

if(test){
if(require(mvMORPH)){
set.seed(1)
n <- 32 # number of species
p <- 31 # number of traits

tree <- pbtree(n=n) # phylogenetic tree
R <- Posdef(p)      # a random symmetric matrix (covariance)

# simulate a dataset
Y <- mvSIM(tree, model="BM1", nsim=1, param=list(sigma=R))

# fit a multivariate Pagel lambda model with Penalized likelihood
fit <- fit_t_pl(Y, tree, model="lambda", method="RidgeAlt")

# Perform a phylogenetic PCA using the model fit (Pagel lambda model)
pca_results <- phyl.pca_pl(fit, plot=TRUE) 

# retrieve the scores
head(pca_results$scores)
}
}