Description Usage Arguments Details Value Note Author(s) References See Also Examples
The function performs an ANOVA like permutation test for Constrained
Correspondence Analysis (cca
), Redundancy Analysis
(rda
) or distancebased Redundancy Analysis
(dbRDA, capscale
) to assess the significance of constraints.
1 2 3 4 5 6 7 8 9 10 
object,x 
A result object from 
alpha 
Targeted Type I error rate. 
beta 
Accepted Type II error rate. 
step 
Number of permutations during one step. 
perm.max 
Maximum number of permutations. 
by 
Setting 
... 
Parameters passed to other functions.

permutations 
Number of permutations for assessing significance of constraints. 
model 
Permutation model (partial match). 
first 
Assess only the significance of the first constrained
eigenvalue; will be passed from 
strata 
An integer vector or factor specifying the strata for permutation. If supplied, observations are permuted only within the specified strata. 
Functions 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
.
The default test is 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 (“partialled
out”) and a test for the first constrained eigenvalues is
performed (Legendre et al. 2011).
You can stop permutation tests after exceeding a given
significance level with argument cutoff
to speed up
calculations in large models. Setting 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. Setting by = "margin"
will perform separate
significance test for each marginal term in a model with all other
terms. The marginal test also accepts a scope
argument for
the drop.scope
which can be a character vector of term
labels that are analysed, or a fitted model of lower scope. The
marginal effects are also known as “Type III” effects, but
the current function only evaluates marginal terms. It will, for
instance, ignore main effects that are included in interaction
terms. In calculating pseudoF, 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 the longest permutation at the
exit from the function.
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 (at the first step, the number of
permutations is step  1
). 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
.
Community data are permuted with choice model="direct"
,
residuals after partial CCA/ RDA/ dbRDA with choice model="reduced"
(default), and residuals after CCA/ RDA/ dbRDA under choice
model="full"
. If there is no partial CCA/ RDA/ dbRDA stage,
model="reduced"
simply permutes the data and is equivalent to
model="direct"
. The test statistic is “pseudoF”,
which is the ratio of constrained and unconstrained total Inertia
(Chisquares, 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
pseudoF and eigenvalues would give equal results. In partial
CCA/ RDA/ dbRDA, the effect of conditioning variables
(“covariables”) is removed before permutation, and these
residuals are added to the nonpermuted fitted values of partial CCA
(fitted values of X ~ Z
). Consequently, the total Chisquare
is not fixed, and test based on pseudoF would differ from the
test based on plain eigenvalues. CCA is a weighted method, and
environmental data are reweighted at each permutation step using
permuted weights.
Function permutest.cca
returns an object of class
"permutest.cca"
, which has its own print
method. The
distribution of permuted F values can be inspected with
density.permutest.cca
function. The function
anova.cca
calls permutest.cca
and fills an
anova
table.
Some cases of anova
need access to the original data on
constraints (at least by = "term"
and by = "margin"
),
and they may fail if data are unavailable.
The default permutation model
changed from "direct"
to
"reduced"
in vegan version 1.150, and you must
explicitly set model = "direct"
for compatibility with the old
version.
Tests by = "terms"
and by = "margin"
are consistent
only when model = "direct"
.
Jari Oksanen
Legendre, P. and Legendre, L. (2012). Numerical Ecology. 3rd English ed. Elsevier.
Legendre, P., Oksanen, J. and ter Braak, C.J.F. (2011). Testing the significance of canonical axes in redundancy analysis. Methods in Ecology and Evolution 2, 269–277.
cca
, rda
, capscale
to get something to analyse. Function drop1.cca
calls
anova.cca
with by = "margin"
, and
add1.cca
an analysis for single terms additions, which
can be used in automatic or semiautomatic model building (see
deviance.cca
).
1 2 3 4 5 6 7 8 9 10 11 12 13  data(varespec)
data(varechem)
vare.cca < cca(varespec ~ Al + P + K, varechem)
## overall test
anova(vare.cca)
## Test for axes
anova(vare.cca, by="axis", perm.max=500)
## Sequential test for terms
anova(vare.cca, by="terms", permu=200)
## Marginal or Type III effects
anova(vare.cca, by="margin")
## Marginal test knows 'scope'
anova(vare.cca, by = "m", scope="P")

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