mrpp {vegan}R Documentation

Multi Response Permutation Procedure of Within- versus Among-Group Dissimilarities

Description

Multiple Response Permutation Procedure (MRPP) provides a test of whether there is a significant difference between two or more groups of sampling units.

Usage

mrpp(dat, grouping, permutations = 1000, distance = "euclidean",
     weight.type = 1, strata)

Arguments

dat data matrix or data frame in which rows are samples and columns are response variable(s), or a dissimilarity object or a symmetric square matrix of dissimilarities.
grouping Factor or numeric index for grouping observations.
permutations Number of permutations to assess the significance of the MRPP statistic, delta.
distance Choice of distance metric that measures the dissimilarity between two observations . See vegdist for options. This will be used if dat was not a dissimilarity structure of a symmetric square matrix.
weight.type choice of group weights. See Details below for options.
strata An integer vector or factor specifying the strata for permutation. If supplied, observations are permuted only within the specified strata.

Details

Multiple Response Permutation Procedure (MRPP) provides a test of whether there is a significant difference between two or more groups of sampling units. This difference may be one of location (differences in mean) or one of spread (differences in within-group distance). Function mrpp operates on a data.frame matrix where rows are observations and responses data matrix. The response(s) may be uni- or multivariate. The method is philosophically and mathematically allied with analysis of variance, in that it compares dissimilarities within and among groups. If two groups of sampling units are really different (e.g. in their species composition), then average of the within-group compositional dissimilarities ought to be less than the average of the dissimilarities between two random collection of sampling units drawn from the entire population.

The mrpp statistic delta is simply the overall weighted mean of within-group means of the pairwise dissimilarities among sampling units. The correct choice of group weights is currently not clear. The mrpp function offers three choices: (1) group size (n), (2) a degrees-of-freedom analogue (n-1), and (3) a weight that is the number of unique distances calculated among n sampling units (n(n-1)/2).

The mrpp algorithm first calculates all pairwise distances in the entire dataset, then calculates delta. It then permutes the sampling units and their associated pairwise distances, and recalculates a delta based on the permuted data. It repeats the permutation step permutations times. The significance test is simply the fraction of permuted deltas that are less than the observed delta, with a small sample correction. The function also calculates the change-corrected within-group agreement A = 1 -delta/E(delta), where E(delta) is the expected delta assessed as the average of permutations.

If the first argument dat can be interpreted as dissimilarities, they will be used directly. In other cases the function treats dat as observations, and uses vegdist to find the dissimilarities. The default distance is Euclidean as in the traditional use of the method, but other dissimilarities in vegdist also are available.

Value

The function returns a list of class mrpp with following items:

call Function call.
delta The overall weighted mean of group mean distances.
E.delta expected delta, under the null hypothesis of no group structure. This is the mean of the permuted deltas.
Pvalue Significance of the test.
A A chance-corrected estimate of the proportion of the distances explained by group identity; a value analogous to a coefficient of determination in a linear model.
distance Choice of distance metric used; the "method" entry of the dist object.
weight.type The choice of group weights used.
boot.deltas The vector of "permuted deltas," the deltas calculated from each of the permuted datasets.
permutations The number of permutations used.

Note

This difference may be one of location (differences in mean) or one of spread (differences in within-group distance). That is, it may find a significant difference between two groups simply because one of those groups has a greater dissimilarities among its sampling units. Most mrpp models can be analysed with adonis which seems not suffer from the same problems as mrpp and is a more robust alternative.

Author(s)

M. Herny H. Stevens HStevens@muohio.edu and Jari Oksanen.

References

P. W. Mielke and K. J. Berry. 2001. Permutation Methods: A Distance Function Approach. Springer Series in Statistics. Springer.

B. McCune and J. B. Grace. 2002. Analysis of Ecological Communities. MjM Software Design, Gleneden Beach, Oregon, USA.

See Also

anosim for a similar test based on ranks, and mantel for comparing dissimilarities against continuous variables, and vegdist for obtaining dissimilarities, adonis is a more robust alternative in most cases.

Examples

data(dune)
data(dune.env)
dune.mrpp <- mrpp(dune, dune.env$Management)
dune.mrpp

# Save and change plotting parameters
def.par <- par(no.readonly = TRUE)
layout(matrix(1:2,nr=1))

plot(dune.ord <- metaMDS(dune), type="text", display="sites" )
ordihull(dune.ord, dune.env$Management)

with(dune.mrpp, {
  fig.dist <- hist(boot.deltas, xlim=range(c(delta,boot.deltas)), 
                 main="Test of Differences Among Groups")
  abline(v=delta); 
  text(delta, 2*mean(fig.dist$counts), adj = -0.5,
     expression(bold(delta)), cex=1.5 )  }
)
par(def.par)

[Package vegan version 1.15-1 Index]