mvgls.dfa {mvMORPH}

Discriminant Function Analysis (DFA) - also called Linear Discriminant Analysis (LDA) or Canonical Variate Analysis (CVA) - based on multivariate GLS (or OLS) model fit

Description

Performs a discriminant analysis (DFA) on a regularized variance-covariance matrix obtained using either the mvgls or mvols function.

Usage

mvgls.dfa(object, ...)

Arguments

object

A model fit obtained by the mvgls or the mvols function.

...

Options to be passed through. (e.g., term="the term corresponding to the factor of interest", type="I" for the type of decomposition of the hypothesis matrix (see also manova.gls) , etc.)

Details

mvgls.dfa allows computing a discriminant analysis based on GLS (or OLS) estimates from a regression model (see mvgls and mvols). Discriminant functions can be used for dimensionality reduction, to follow up a MANOVA analysis to describe group separation, or for group prediction.

Value

a list with the following components

coeffs

a matrix containing the raw discriminants

coeffs.std

a matrix containing the standardized discriminants

scores

a matrix containing the discriminant scores [residuals X coeffs]

residuals

the centered [with GLS or OLS] response variables

H

the hypothesis (or between group model matrix)

E

the error (or residual model matrix)

rank

the rank of HE^{-1}

pct

the percentage of the discriminant functions

Note

Still in development, may not handle special designs.

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.

Clavel, J., Morlon, H., 2020. Reliable phylogenetic regressions for multivariate comparative data: illustration with the MANOVA and application to the effect of diet on mandible morphology in Phyllostomid bats. Systematic Biology 69(5): 927-943.

See Also

mvgls, mvols, manova.gls, mvgls.pca, predict.mvgls.dfa,

Examples

library(mvMORPH)
n=64
p=4

tree <- pbtree(n=n)
sigma <- crossprod(matrix(runif(p*p),p,p))
resid <- mvSIM(tree, model="BM1", param=list(sigma=sigma))
Y <- rep(c(0,1.5), each=n/2) + resid
grp <- as.factor(rep(c("gp1","gp2"),each=n/2))
names(grp) = rownames(Y)
data <- list(Y=Y, grp=grp)
mod <- mvgls(Y~grp, data=data, tree=tree, model="BM")

# fda
da1 <- mvgls.dfa(mod)

plot(da1)