mvgls.pca {mvMORPH}

Principal Component Analysis (PCA) based on GLS (or OLS) 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 or the mvols function. With "evolutionary" models in mvgls, this performs the so-called phylogenetic PCA.

Usage

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

Arguments

object

A model fit obtained by the mvgls or mvols 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

mvgls.pca allows computing a principal component analysis based on a GLS (or OLS) estimate of the covariance matrix (see mvgls and mvols). 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 fit reduce this bias and allow incorporating various residuals structures (see Clavel et al. 2019). Plotting 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

scores

the PC scores

values

the eigenvalues of the variance-covariance matrix estimated by mvgls or mvols

vectors

the eigenvectors of the variance-covariance matrix estimated by mvgls or mvols

rank

the rank of the estimated variance-covariance matrix

Note

Contrary to conventional PCA (for instance using mvols with "LL" method), the principal axes of the gls PCA are not orthogonal, they represent the main axes of independent (according to a given phylogenetic or time-series model) evolutionary changes.

Author(s)

J. Clavel

References

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. Systematic Biology 68(1): 93-116.

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

See Also

mvgls, mvols, GIC, EIC

Examples

set.seed(1)
n <- 32 # number of species
p <- 30 # number of traits

tree <- pbtree(n=n) # phylogenetic tree
R <- crossprod(matrix(runif(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=TRUE) 




# 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=TRUE) 

# retrieve the scores
head(pca_results$scores)