effectsize: Multivariate measure of association/effect size for objects...

In JClavel/mvMORPH: Multivariate Comparative Tools for Fitting Evolutionary Models to Morphometric Data

Multivariate measure of association/effect size for objects of class "manova.gls"

Description

This function estimate the multivariate effectsize for all the outcomes variables of a multivariate analysis of variance

Usage

effectsize(x,...)

Arguments

x	An object of class "manova.gls"
...	One can specify adjusted=TRUE to obtain Serlin' adjustment to Pillai trace effect size, or Tatsuoka' adjustment for Wilks' lambda. These adjustments are correcting positive bias with increasing number of variables.

Details

This function allows estimating multivariate effect size / multivariate measure of association for the four multivariate statistics implemented in manova.gls (Pillai, Wilks, Roy, Hotelling-Lawley). These multivariate measures are common generalizations of univariate measures such as the squared-multiple correlation, with values ranging between 0 and 1 (see for instance details in Rencher 2002). Note that these measures are known to be upwardly biased with increased dimensionality (Kim and Olejnik 2005), and several adjustments were proposed (e.g., Serlin 1982, Tatsuoka 1973; see adjusted=TRUE argument above). For models fit by PL, the adjustments is done by estimating the bias from the permuted statistics under the null. Note that adjusted measures might be sligthly negative, in such a case the measure should be interpreted as virtually 0 (accordingly, statistical tests from the manova.gls function should be non-significant in these situations).

Value

Return the effect size for all the terms of the MANOVA or pairwise tests.

Note

This function is still under development.

Author(s)

Julien Clavel

References

Clavel et al. in prep.

Kim, S., Olejnik S., 2005. Bias and precision of measures of association for a fixed-effect multivariate analysis of variance model. Multivariate Behavioral Research, 40(4):401-421.

Rencher, 2002. Methods of Multivariate Analysis (Second Edition). Wiley and Sons. pp. 705.

Serlin, R. C., 1982. A multivariate measure of association based on the Pillai-Bartlett procedure. Psycological Bulletin 91(2):413-417.

Tatsuoka, M. M. 1973. An examination of the statistical properties of a multivariate measure of strength of relationship (final report). Project No. 2-E-020, Grant No. OEG-5-72-0027(509).

See Also

manova.gls mvgls mvols pairwise.glh

Examples

set.seed(123)
n <- 32 # number of species
p <- 3  # 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))
X <- rnorm(n) # continuous
grp <- rep(1:2, each=n/2)
dataset <- list(y=Y, x=X, grp=as.factor(grp))

# Model fit
model1 <- mvgls(y~x+grp, data=dataset, tree=tree, model="BM", method="LL")

# Multivariate test
(multivariate_test <- manova.gls(model1, test="Pillai"))
effectsize(multivariate_test)

JClavel/mvMORPH documentation built on Feb. 14, 2025, 6:27 a.m.