anova.cca  R Documentation 
The function performs an ANOVA like permutation test for Constrained
Correspondence Analysis (cca
), Redundancy Analysis
(rda
) or distancebased Redundancy Analysis (dbRDA,
dbrda
) to assess the significance of constraints.
## S3 method for class 'cca'
anova(object, ..., permutations = how(nperm=999),
by = NULL, model = c("reduced", "direct", "full"),
parallel = getOption("mc.cores"), strata = NULL,
cutoff = 1, scope = NULL)
## S3 method for class 'cca'
permutest(x, permutations = how(nperm = 99),
model = c("reduced", "direct", "full"), by = NULL, first = FALSE,
strata = NULL, parallel = getOption("mc.cores"), ...)
object 
One or several result objects from 
x 
A single ordination result object. 
permutations 
a list of control values for the permutations
as returned by the function 
by 
Setting 
model 
Permutation model: 
parallel 
Use parallel processing with the given number of cores. 
strata 
An integer vector or factor specifying the strata for
permutation. If supplied, observations are permuted only within
the specified strata. It is an error to use this when

cutoff 
Only effective with 
scope 
Only effective with 
first 
Analyse only significance of the first axis. 
... 
Parameters passed to other functions. 
Functions anova.cca
and permutest.cca
implement ANOVA
like permutation tests for the joint effect of constraints in
cca
, rda
, dbrda
or
capscale
. Function anova
is intended as a more
userfriendly alternative to permutest
(that is the real
workhorse).
Function anova
can analyse a sequence of constrained
ordination models. The analysis is based on the differences in
residual deviance in permutations of nested models.
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 = "onedf"
will
perform a similar sequential test for onedegreeoffreedom effects,
where multilevel factors are split in their contrasts. 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.
Community data are permuted with choice model="direct"
, and
residuals after partial CCA/ RDA/ dbRDA with choice
model="reduced"
(default). 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 degrees of freedom. 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 the total Chisquare is not fixed, and test based on
pseudoF
would differ from the test based on plain
eigenvalues.
The function anova.cca
calls permutest.cca
and fills an
anova
table. Additional attributes are
Random.seed
(the random seeds used),
control
(the permutation design, see how) and
F.perm
(the permuted test statistics).
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.
anova.cca
, cca
,
rda
, dbrda
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
).
data(dune, dune.env)
mod < cca(dune ~ Moisture + Management, dune.env)
## overall test
anova(mod)
## tests for individual terms
anova(mod, by="term")
anova(mod, by="margin")
## sequential test for contrasts
anova(mod, by = "onedf")
## test for adding all environmental variables
anova(mod, cca(dune ~ ., dune.env))
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