vegan (version 1.11-0)

mantel: Mantel and Partial Mantel Tests for Dissimilarity Matrices

Description

Function mantel finds the Mantel statistic as a matrix correlation between two dissimilarity matrices, and function mantel.partial finds the partial Mantel statistic as the partial matrix correlation between three dissimilarity matricies. The significance of the statistic is evaluated by permuting rows and columns of the first dissimilarity matrix.

Usage

mantel(xdis, ydis, method="pearson", permutations=1000, strata)
mantel.partial(xdis, ydis, zdis, method = "pearson", permutations = 1000, 
    strata)

Arguments

xdis, ydis, zdis

Dissimilarity matrices or a dist objects.

method

Correlation method, as accepted by cor: "pearson", "spearman" or "kendall".

permutations

Number of permutations in assessing significance.

strata

An integer vector or factor specifying the strata for permutation. If supplied, observations are permuted only within the specified strata.

Value

• The function returns a list of class mantel with following components:
• Call
  Function call.
• method
  Correlation method used, as returned by cor.test.
• statistic
  The Mantel statistic.
• signif
  Empirical significance level from permutations.
• perm
  A vector of permuted values.
• permutations
  Number of permutations.

Details

Mantel statistic is simply a correlation between entries of two dissimilarity matrices (some use cross products, but these are linearly related). However, the significance cannot be directly assessed, because there are $N(N-1)/2$ entries for just $N$ observations. Mantel developed asymptotic test, but here we use permutations of $N$ rows and columns of dissimilarity matrix.

Partial Mantel statistic uses partial correlation conditioned on the third matrix. Only the first matrix is permuted so that the correlation structure between second and first matrices is kept constant. Although mantel.partial silently accepts other methods than "pearson", partial correlations will probably be wrong with other methods.

The function uses cor, which should accept alternatives pearson for product moment correlations and spearman or kendall for rank correlations.

References

The test is due to Mantel, of course, but the current implementation is based on Legendre and Legendre.

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

See Also

cor for correlation coefficients, protest (``Procrustes test'') for an alternative with ordination diagrams, anosim and mrpp for comparing dissimilarities against classification. For dissimilarity matrices, see vegdist or dist. See bioenv for selecting environmental variables.

Examples

## Is vegetation related to environment?
data(varespec)
data(varechem)
veg.dist <- vegdist(varespec) # Bray-Curtis
env.dist <- vegdist(scale(varechem), "euclid")
mantel(veg.dist, env.dist)
mantel(veg.dist, env.dist, method="spear")