Nested Analysis of Variance via Distance-based Redundancy Analysis or Non-parametric Multivariate Analysis of Variance

Description

The functions provide nested analysis of variance for a two-level hierarchical model. The functions are implemented by estimating the correct F-ratio for the main and nested factors (assuming the nested factor is random) and using the recommended permutation procedures to test the significance of these F-ratios. F-ratios are estimated from variance estimates that are provided by distance-based redundancy analysis (capscale) or non-parametric multivariate analysis of variance (adonis).

Usage

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nested.anova.dbrda(formula, data, method="euc", add=FALSE,
    permutations=100, warnings=FALSE)
nested.npmanova(formula, data, method="euc", permutations=100, warnings=FALSE)

Arguments

formula

Formula with a community data frame (with sites as rows, species as columns and species abundance as cell values) or (for nested.anova.dbrda only) distance matrix on the left-hand side and two categorical variables on the right-hand side (with the second variable assumed to be nested within the first).

data

Environmental data set.

method

Method for calculating ecological distance with function vegdist: partial match to "manhattan", "euclidean", "canberra", "bray", "kulczynski", "jaccard", "gower", "morisita", "horn" or "mountford". This argument is ignored in case that the left-hand side of the formula already is a distance matrix.

add

Should a constant be added to the off-diagonal elements of the distance-matrix (TRUE) or not.

permutations

The number of permutations for significance testing.

warnings

Should warnings be suppressed (TRUE) or not.

Details

The functions provide two alternative procedures for multivariate analysis of variance on the basis of any distance measure. Function nested.anova.dbrda proceeds via capscale, whereas nested.npmanova proceeds via adonis. Both methods are complementary to each other as nested.npmanova always provides correct F-ratios and estimations of significance, whereas nested.anova.dbrda does not provide correct F-ratios and estimations of significance when negative eigenvalues are encountered or constants are added to the distance matrix, but always provides an ordination diagram.

The F-ratio for the main factor is estimated as the mean square of the main factor divided by the mean square of the nested factor. The significance of the F-ratio of the main factor is tested by permuting entire blocks belonging to levels of the nested factor. The significance of the F-ratio of the nested factor is tested by permuting sample units within strata defined by levels of the main factor.

Value

The functions provide an ANOVA table.

Author(s)

Roeland Kindt (World Agroforestry Centre)

References

Legendre, P. & Anderson, M. J. (1999). Distance-based redundancy analysis: testing multispecies responses in multifactorial ecological experiments. Ecological Monographs 69, 1-24.

Anderson, M.J. (2001). A new method for non-parametric multivariate analysis of variance. Austral Ecology, 26: 32-46.

McArdle, B.H. and M.J. Anderson. (2001). Fitting multivariate models to community data: A comment on distance-based redundancy analysis. Ecology, 82: 290-297.

Examples

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## Not run: 
library(vegan)
data(warcom)
data(warenv)
# use larger number of permutations for real studies
nested.npmanova(warcom~rift.valley+popshort, data=warenv, method="jac", 
    permutations=5)
nested.anova.dbrda(warcom~rift.valley+popshort, data=warenv, method="jac", 
    permutations=5)

## End(Not run)

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