cca), Redundancy Analysis
(rda) or Constrained Analysis of Principal Coordinates
(capscale) to assess the significance of constraints.## S3 method for class 'cca':
anova(object, alpha=0.05, beta=0.01, step=100, perm.max=10000,
by = NULL, ...)
permutest.cca(x, permutations=100, model=c("direct", "reduced","full"),
first = FALSE, strata, ...)cca.by = "axis" will assess significance for each
constrained axis, and setting by = "terms" will asses
significance for each term (sequentially from first to last).anova.cca.permutest.cca returns an object of class
permutest.cca which has its own print method. The
function anova.cca calls permutest.cca, fills an
anova table and uses print.anova for printing.anova.cca and permutest.cca implement an ANOVA
like permutation test for the joint effect of constraints in
cca, rda or capscale.
Functions anova.cca and permutest.cca differ in printout
style and in interface.
Function permutest.cca is the proper workhorse, but
anova.cca passes all parameters to permutest.cca. In anova.cca the number of permutations is controlled by
targeted ``critical'' $P$ value (alpha) and accepted Type
II or rejection error (beta). If the results of permutations
differ from the targeted alpha at risk level given by
beta, the permutations are
terminated. If the current estimate of $P$ does not
differ significantly from alpha of the alternative hypothesis,
the permutations are
continued with step new permutations. However, with by =
"terms" a fixed number of permutations will be used, and this
is given by argument permutations, or if this is missing,
by step.
The function permutest.cca implements a permutation test for
the ``significance'' of constraints in cca,
rda or capscale. Community data are
permuted with choice model = "direct", residuals after
partial CCA/RDA/CAP with choice model = "reduced",
and residuals after CCA/RDA/CAP under choice model = "full".
If there is no partial CCA/RDA/CAP stage, model = "reduced" simply permutes
the data. The test statistic is ``pseudo-$F$'', which is the ratio
of constrained and unconstrained total Inertia (Chi-squares, variances
or something similar), each divided by their respective ranks. If
there are no conditions ("partial" terms),
the sum of all eigenvalues
remains constant, so that pseudo-$F$ and eigenvalues would give
equal results. In partial CCA/RDA/CAP, the effect of conditioning variables
(``covariables'') is removed before permutation, and these residuals
are added to the non-permuted fitted values of partial CCA (fitted
values of X ~ Z). Consequently, the total Chi-square is not
fixed, and test based on pseudo-$F$ would differ from the test based on
plain eigenvalues. CCA is a weighted method, and environmental data
are re-weighted at each permutation step using permuted weights.
Default test will be for the sum of all constrained eigenvalues.
Setting first = TRUE will perform a test for the first
constrained eigenvalue. Argument first can be set either in
anova.cca or in permutest.cca. It is also possible to
perform significance tests for each axis or for each term (constraining
variable) using argument by in anova.cca.
Setting by = "axis" will perform separate significance tests
for each constrained axis. All previous constrained axes will be used
as conditions (by = "terms" will
perform separate
significance test for each term (constraining variable). The terms are
assessed sequentially from first to last, and the order of the terms
will influence their significances. In calculating pseudo-$F$, all
terms are compared to the same residual of the full model.
Permutations for all axes or terms will
start from the same .Random.seed, and the seed will be
advanced to the value after longest permutation at the exit from the
function.
cca, rda, capscale.data(varespec)
data(varechem)
vare.cca <- cca(varespec ~ Al + P + K, varechem)
anova(vare.cca)
anova(vare.cca, by="axis", perm.max=500)
anova(vare.cca, by="terms", permu=200)Run the code above in your browser using DataLab