mvgls.pca | R Documentation |
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.
mvgls.pca(object, plot=TRUE, ...)
object |
A model fit obtained by the |
plot |
Plot of the PC's axes. Default is TRUE (see details).' |
... |
Options to be passed through. (e.g., |
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.
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 |
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.
J. Clavel
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.
mvgls
,
mvols
,
GIC
,
EIC
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)
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