Description Usage Arguments Details Value Note Author(s) References See Also Examples
Multiple Response Permutation Procedure (MRPP) provides a
test of whether there is a significant difference between two or more
groups of sampling units. Function meandist
finds the mean within
and between block dissimilarities.
1 2 3 4 5 6 7 8  mrpp(dat, grouping, permutations = 999, distance = "euclidean",
weight.type = 1, strata = NULL, parallel = getOption("mc.cores"))
meandist(dist, grouping, ...)
## S3 method for class 'meandist'
summary(object, ...)
## S3 method for class 'meandist'
plot(x, kind = c("dendrogram", "histogram"), cluster = "average",
ylim, axes = TRUE, ...)

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 
a list of control values for the permutations
as returned by the function 
distance 
Choice of distance metric that measures the
dissimilarity between two observations . See 
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. 
parallel 
Number of parallel processes or a predefined socket
cluster. With 
dist 
A 
.
object, x 
A 
kind 
Draw a dendrogram or a histogram; see Details. 
cluster 
A clustering method for the 
ylim 
Limits for vertical axes (optional). 
axes 
Draw scale for the vertical axis. 
... 
Further arguments passed to functions. 
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 withingroup distance;
cf. Warton et al. 2012). 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 withingroup
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 δ is the overall weighted mean of
withingroup means of the pairwise dissimilarities among sampling
units. The choice of group weights is currently not clear. The
mrpp
function offers three choices: (1) group size (n),
(2) a degreesoffreedom analogue (n1), and (3) a weight that
is the number of unique distances calculated among n sampling
units (n(n1)/2).
The mrpp
algorithm first calculates all pairwise distances in
the entire dataset, then calculates δ. It then permutes the
sampling units and their associated pairwise distances, and
recalculates δ based on the permuted data. It repeats the
permutation step permutations
times. The significance test is
the fraction of permuted deltas that are less than the observed delta,
with a small sample correction. The function also calculates the
changecorrected withingroup agreement A = 1 δ/E(δ),
where E(δ) is the expected δ assessed as the
average of dissimilarities.
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.
Function meandist
calculates a matrix of mean withincluster
dissimilarities (diagonal) and betweencluster dissimilarities
(offdiagonal elements), and an attribute n
of grouping
counts. Function summary
finds the withinclass, betweenclass
and overall means of these dissimilarities, and the MRPP statistics
with all weight.type
options and the Classification Strength,
CS (Van Sickle and Hughes, 2000). CS is defined for dissimilarities as
BbarWbar, where Bbar is the
mean between cluster dissimilarity and Wbar is the mean
within cluster dissimilarity with weight.type = 1
. The function
does not perform significance tests for these statistics, but you must
use mrpp
with appropriate weight.type
. There is
currently no significance test for CS, but mrpp
with
weight.type = 1
gives the correct test for Wbar
and a good approximation for CS. Function plot
draws a
dendrogram or a histogram of the result matrix based on the
withingroup and between group dissimilarities. The dendrogram is
found with the method given in the cluster
argument using
function hclust
. The terminal segments hang to
withincluster dissimilarity. If some of the clusters are more
heterogeneous than the combined class, the leaf segment are reversed.
The histograms are based on dissimilarities, but ore otherwise similar
to those of Van Sickle and Hughes (2000): horizontal line is drawn at
the level of mean betweencluster dissimilarity and vertical lines
connect withincluster dissimilarities to this line.
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 and Hughes,
2000). Currently not implemented and always 
n 
Number of observations in each class. 
classdelta 
Mean dissimilarities within classes. The overall
δ is the weighted average of these values with given

.
Pvalue 
Significance of the test. 
A 
A chancecorrected 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. The distribution of
this item can be inspected with 
permutations 
The number of permutations used. 
control 
A list of control values for the permutations
as returned by the function 
This difference may be one of location (differences in mean) or one of
spread (differences in withingroup 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.
M. Henry H. Stevens HStevens@muohio.edu and Jari Oksanen.
B. McCune and J. B. Grace. 2002. Analysis of Ecological Communities. MjM Software Design, Gleneden Beach, Oregon, USA.
P. W. Mielke and K. J. Berry. 2001. Permutation Methods: A Distance Function Approach. Springer Series in Statistics. Springer.
J. Van Sickle and R. M. Hughes 2000. Classification strengths of ecoregions, catchments, and geographic clusters of aquatic vertebrates in Oregon. J. N. Am. Benthol. Soc. 19:370–384.
Warton, D.I., Wright, T.W., Wang, Y. 2012. Distancebased multivariate analyses confound location and dispersion effects. Methods in Ecology and Evolution, 3, 89–101
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.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26  data(dune)
data(dune.env)
dune.mrpp < with(dune.env, mrpp(dune, 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" )
with(dune.env, ordihull(dune.ord, 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)
## meandist
dune.md < with(dune.env, meandist(vegdist(dune), Management))
dune.md
summary(dune.md)
plot(dune.md)
plot(dune.md, kind="histogram")

Loading required package: permute
Loading required package: lattice
This is vegan 2.43
Call:
mrpp(dat = dune, grouping = Management)
Dissimilarity index: euclidean
Weights for groups: n
Class means and counts:
BF HF NM SF
delta 10.03 11.08 10.66 12.27
n 3 5 6 6
Chance corrected withingroup agreement A: 0.1246
Based on observed delta 11.15 and expected delta 12.74
Significance of delta: 0.001
Permutation: free
Number of permutations: 999
Run 0 stress 0.1192678
Run 1 stress 0.219292
Run 2 stress 0.1192679
... Procrustes: rmse 8.820187e05 max resid 0.0002625276
... Similar to previous best
Run 3 stress 0.1183186
... New best solution
... Procrustes: rmse 0.0202672 max resid 0.06494471
Run 4 stress 0.1183186
... Procrustes: rmse 8.415528e05 max resid 0.0002703275
... Similar to previous best
Run 5 stress 0.1809579
Run 6 stress 0.1808913
Run 7 stress 0.2075713
Run 8 stress 0.2465148
Run 9 stress 0.1183186
... New best solution
... Procrustes: rmse 2.533113e05 max resid 7.662459e05
... Similar to previous best
Run 10 stress 0.1183186
... Procrustes: rmse 1.948304e05 max resid 6.912645e05
... Similar to previous best
Run 11 stress 0.1183186
... Procrustes: rmse 0.000123975 max resid 0.0004025931
... Similar to previous best
Run 12 stress 0.1183186
... Procrustes: rmse 9.693875e05 max resid 0.0003189633
... Similar to previous best
Run 13 stress 0.1192678
Run 14 stress 0.1183186
... Procrustes: rmse 9.748507e06 max resid 3.252465e05
... Similar to previous best
Run 15 stress 0.1192685
Run 16 stress 0.1889658
Run 17 stress 0.1809582
Run 18 stress 0.1192684
Run 19 stress 0.1192679
Run 20 stress 0.1192679
*** Solution reached
BF HF NM SF
BF 0.4159972 0.4736637 0.7296979 0.6247169
HF 0.4736637 0.4418115 0.7217933 0.5673664
NM 0.7296979 0.7217933 0.6882438 0.7723367
SF 0.6247169 0.5673664 0.7723367 0.5813015
attr(,"class")
[1] "meandist" "matrix"
attr(,"n")
grouping
BF HF NM SF
3 5 6 6
Mean distances:
Average
within groups 0.5746346
between groups 0.6664172
overall 0.6456454
Summary statistics:
Statistic
MRPP A weights n 0.1423836
MRPP A weights n1 0.1339124
MRPP A weights n(n1) 0.1099842
Classification strength 0.1127012
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