The function performs an ANOVA like permutation test for Constrained
Correspondence Analysis (
cca), Redundancy Analysis
rda) or distance-based Redundancy Analysis (dbRDA,
capscale) to assess the significance of constraints.
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## 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"), first = FALSE, strata = NULL, parallel = getOption("mc.cores"), ...)
One or several result objects from
A single ordination result object.
a list of control values for the permutations
as returned by the function
Use parallel processing with the given number of cores.
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
Only effective with
Only effective with
Analyse only significance of the first axis.
Parameters passed to other functions.
ANOVA like permutation tests for the joint effect of constraints in
permutest.cca differ in
printout style and in interface. Function
the proper workhorse, but
anova.cca passes all parameters to
anova can analyse a sequence of constrained
ordination models. The analysis is based on the differences in
residual deviances in permutations of nested models.
The default test is for the sum of all constrained eigenvalues.
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 = "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
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
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 pseudo-F, all terms are compared to the
same residual of the full model.
Community data are permuted with choice
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
“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/ dbRDA, 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.
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).
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.
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.
capscale to get something to
by = "margin", and
add1.cca an analysis
for single terms additions, which can be used in automatic or
semiautomatic model building (see
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Loading required package: permute Loading required package: lattice This is vegan 2.4-3 Permutation test for cca under reduced model Permutation: free Number of permutations: 999 Model: cca(formula = varespec ~ Al + P + K, data = varechem) Df ChiSquare F Pr(>F) Model 3 0.64413 2.984 0.001 *** Residual 20 1.43906 --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
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