mvMORPH (version 1.1.0)

mvgls.pca: Principal Component Analysis (PCA) based on GLS estimate of the traits variance-covariance matrix (possibly regularized).

Description

Performs a principal component analysis (PCA) on a regularized variance-covariance matrix obtained using the mvgls function. With "evolutionary" models, this performs the so-called phylogenetic PCA.

Usage

mvgls.pca(object, plot=TRUE, ...)

Arguments

object

A model fit obtained by the mvgls 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.)

Value

a list with the following components

scores

the PC scores

values

the eigenvalues of the variance-covariance matrix estimated by mvgls

vectors

the eigenvectors of the variance-covariance matrix estimated by mvgls

rank

the rank of the estimated variance-covariance matrix

Details

mvgls.pca allows computing a principal component analysis based on a GLS estimate of the covariance matrix (see mvgls). The phylogenetic PCA (following Revell 2009) is a special case obtained from the (possibly regularized) evolutionary variance-covariance matrix (see also the phyl.pca_pl function in RPANDA). In the high-dimensional case the contribution of the firsts PC axes tend to be overestimated with traditional maximum likelihood approaches. Penalized/regularized model fits reduce this bias and allow the estimation of various error structure models (see Clavel et al. 2018). 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.

References

Clavel, J., Aristide, L., Morlon, H., 2018. A Penalized Likelihood framework for high-dimensional phylogenetic comparative methods and an application to new-world monkeys brain evolution. Systematic Biology DOI:10.1093/sysbio/syy045.

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

See Also

mvgls, GIC

Examples

# NOT RUN {
set.seed(1)
n <- 32 # number of species
p <- 30 # number of traits

tree <- pbtree(n=n) # phylogenetic tree
R <- crossprod(matrix(rnorm(p*p),p))  # a random symmetric matrix (covariance)

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

# The conventional phylogenetic PCA
phylo_pca <- mvgls(Y~1, tree=tree, model="BM", method="LL")
mvgls.pca(phylo_pca, plot=T) 




# fit a multivariate Pagel lambda model with Penalized likelihood
fit <- mvgls(Y~1, tree=tree, model="lambda", method="LOO", penalty="RidgeAlt")

# Perform a regularized phylogenetic PCA using the model fit (Pagel lambda model)
pca_results <- mvgls.pca(fit, plot=T) 

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