R: Mantel test

mantel {ecodist} | R Documentation

## Mantel test

### Description

Simple and partial Mantel tests, with options for ranked data, permutation tests, and bootstrapped confidence limits.

### Usage

    mantel(formula = formula(data), data, nperm = 1000,
        mrank = FALSE, nboot = 500, pboot = 0.9, cboot = 0.95)

### Arguments

`formula` | formula describing the test to be conducted. For this test, y ~ x will perform a simple Mantel test, while y ~ x + z1 + z2 + z3 will do a partial Mantel test of the relationship between x and y given z1, z2, z3. All variables can be either a distance matrix of class dist or vectors of dissimilarities.
`data` | an optional dataframe containing the variables in the model as columns of dissimilarities. By default the variables are taken from the current environment.
`nperm` | number of permutations to use. If set to 0, the permutation test will be omitted.
`mrank` | if this is set to FALSE (the default option), Pearson correlations will be used. If set to TRUE, the Spearman correlation (correlation ranked distances) will be used.
`nboot` | number of iterations to use for the bootstrapped confidence limits. If set to 0, the bootstrapping will be omitted.
`pboot` | the level at which to resample the data for the bootstrapping procedure.
`cboot` | the level of the confidence limits to estimate.

### Details

If only one independent variable is given, the simple Mantel r (r12) is calculated. If more than one independent variable is given, the partial Mantel r (ryx|x1 ...) is calculated by permuting one of the original dissimilarity matrices. The bootstrapping is actually resampling without replacement, because duplication of samples is not useful in a dissimilarity context (the dissimilarity of a sample with itself is zero). Resampling within dissimilarity values is inappropriate, just as for permutation.

### Value

`mantelr` | Mantel coefficient.
`pval1` | one-tailed p-value (null hypothesis: r <= 0).
`pval2` | one-tailed p-value (null hypothesis: r >= 0).
`pval3` | two-tailed p-value (null hypothesis: r = 0).
`llim` | lower confidence limit.
`ulim` | upper confidence limit.

### Author(s)

Sarah Goslee

### References

Mantel, N. 1967. The detection of disease clustering and a generalized regression approach. Cancer Research 27:209-220.

Smouse, P.E., J.C. Long and R.R. Sokal. 1986. Multiple regression and correlation extensions of the Mantel test of matrix correspondence. Systematic Zoology 35:62 7-632.

Goslee, S.C. and Urban, D.L. 2007. The ecodist package for dissimilarity-based analysis of ecological data. Journal of Statistical Software 22(7):1-19.

Goslee, S.C. 2010. Correlation analysis of dissimilarity matrices. Plant Ecology 206(2):279-286.

### See Also

`mgram`, `mgroup`

### Examples

    data(graze)

    grasses <- graze[, colnames(graze) %in% c("DAGL", "LOAR10", "LOPE", "POPR")]
    legumes <- graze[, colnames(graze) %in% c("LOCO6", "TRPR2", "TRRE3")]

    grasses.bc <- bcdist(grasses)
    legumes.bc <- bcdist(legumes)

    space.d <- dist(graze$sitelocation)
    forest.d <- dist(graze$forestpct)

    # Mantel test: is the difference in forest cover between sites
    # related to the difference in grass composition between sites?
    mantel(grasses.bc ~ forest.d)

    # Mantel test: is the geographic distance between sites
    # related to the difference in grass composition between sites?
    mantel(grasses.bc ~ space.d)

    # Partial Mantel test: is the difference in forest cover between sites
    # related to the difference in grass composition once the
    # linear effects of geographic distance are removed?
    mantel(grasses.bc ~ forest.d + space.d)

    # Mantel test: is the difference in forest cover between sites
    # related to the difference in legume composition between sites?
    mantel(legumes.bc ~ forest.d)

    # Mantel test: is the geographic distance between sites
    # related to the difference in legume composition between sites?
    mantel(legumes.bc ~ space.d)

    # Partial Mantel test: is the difference in forest cover between sites
    # related to the difference in legume composition once the
    # linear effects of geographic distance are removed?
    mantel(legumes.bc ~ forest.d + space.d)

    # Is there nonlinear pattern in the relationship with geographic distance?
    par(mfrow=c(2, 1))
    plot(mgram(grasses.bc, space.d, nclass=8))
    plot(mgram(legumes.bc, space.d, nclass=8))

[Package ecodist version 2.0.7 Index]