vegan (version 1.6-0)

anova.cca: Permutation Test for Constrained Correspondence Analysis, Redundancy Analysis and Constrained Analysis of Principal Coordinates

Description

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.

Usage

## S3 method for class 'cca':
anova(object, alpha=0.05, beta=0.1, step=100, perm.max=2000, ...)
permutest.cca(x, permutations=100, model=c("reduced","full"), strata)

Arguments

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.

Value

• Function permutest.cca returns an object of class permutest.cca which has its own print method. The function anova.cca fills in an anova table and uses print.anova for printing.

Details

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. Residuals after partial CCA/RDA/CAP are permuted with choice model = "reduced", and residuals after CCA/RDA/CAP under choice model = "full". If there is no partial CCA/RDA/CAP stage, the former 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. In plain CCA/RDA/CAP under reduced model, the community data is permuted, and 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.

References

Legendre, P. and Legendre, L. (1998). Numerical Ecology. 2nd English ed. Elsevier.

See Also

cca, rda, capscale.

Examples

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)