mantel {ecodist}

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))