asbio (version 0.2-1)

Mrpp: Multi-response permutation procedure. A wrapper for mrpp from vegan.

Description

While mrpp in library vegan directly tests the hypothesis of identical multivariate disributions using a permutation procedure, PC-ORD approximates the distribution of using a Pearson type III distribution which accommodates the fact that the permutation distribution is often significantly skewed (McCune and Grace 2002). The Pearson type III distribution is similar to the binomial distribution when p $\neq$ q (Abramowitz and Stegun 1972).

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

Factor or numeric index for grouping observations.

distance

Choice of distance metric that measures the dissimilarity between two observations . The function vegdist is used to calculate dissimilarities.

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.

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 original dissimilarities.
• CS
  Classification strength (Van Sickle 1997) with weight.type = 3 and NA with other weights.
• n
  Number of observations in each class.
• classdelta
  Mean dissimilarities within classes. The overall delta is the weighted average of these values with given weight.type.
• Pvalue
  Significance of the test.
• 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.

Details

Mrpp provides additional output to mrpp including a T statistic and a Pearson's type III p-value. The Pearson Type III distribution has three parameters: a mean, standard deviation , and a shape parameter , based on the skewness of the empirical distribution. These are estimated, and p-values are calculated in the wrapper function Mrpp using functions from the library lmomco (Asquith 2008). See documentation from mrpp for additional information.

References

McCune, B. and Grace, J. B. (2002) Analysis of Ecological Communities. MjM Software Design, Gleneden Beach, Oregon, USA. Mielke P. W. and Berry, K. J. (2001) Permutation Methods: A Distance Function Approach. Springer Series in Statistics. Springer. Van Sickle, J. (1997) Using mean similarity dendrograms to evaluate classifications. Journal of Agricultural, Biological, and Environmental Statistics 2:370-388.

Examples

library(vegan)
data(dune)
data(dune.env)
Mrpp(dune, dune.env$Management)