anova.cca {vegan} | R Documentation |
The function performs an ANOVA like permutation test for Constrained
Correspondence Analysis (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, ...) permutest.cca(x, permutations=100, model=c("direct", "reduced","full"), strata)
object,x |
A result object from cca . |
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. |
... |
Parameters to permutest.cca. |
permutations |
Number of permutations for assessing significance of constraints. |
model |
Permutation model (partial match). |
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
.
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.
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.
Function 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.
Jari Oksanen
Legendre, P. and Legendre, L. (1998). Numerical Ecology. 2nd English ed. Elsevier.
data(varespec) data(varechem) vare.cca <- cca(varespec ~ Al + P + K, varechem) anova(vare.cca) permutest.cca(vare.cca) ## Test for adding variable N to the previous model: anova(cca(varespec ~ N + Condition(Al + P + K), varechem), step=40)