mrpp(dat, grouping, permutations = 999, distance = "euclidean",
weight.type = 1, strata)
meandist(dist, grouping, ...)
## S3 method for class 'meandist':
summary(object, ...)
## S3 method for class 'meandist':
plot(x, cluster = "average", ...)vegdist for
options. This will be used if dat was not a dissimilarity
structure of a symmetmeandist result object.hclust
function. Any hclust method can be used, but perhaps only
"average" and "single" make sense.weight.type = 3 and NA with other weights.weight.typemrpp 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.
With weight.type = 3, the function also calculates classification
strength (Van Sickle 1997) which is defined as the difference between
average between group dissimilarities and within group
dissimilarities. With weight.type = 3 the classification strength
is a simple transformation of $\delta$, and has the same permutation
significance.
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 within-cluster
dissimilarities (diagonal) and between-cluster dissimilarites
(off-diagonal elements), and an attribute n of grouping
counts. Function summary finds the within-class, between-class
and overall means of these dissimilarities, and the MRPP statistics
with all weight.type options and the classification
strength. The function does not allow significance tests for these
statistics, but you must use mrpp with appropriate
weight.type. Function plot draws a dendrogram of the
result matrix with given cluster method (see
hclust). The terminal segments hang to within-cluster
dissimilarity. If some of the clusters is more heterogeneous than the
combined class, the leaf segment is reversed.
P. W. Mielke and K. J. Berry. 2001. Permutation Methods: A Distance Function Approach. Springer Series in Statistics. Springer.
J. Van Sickle 1997. Using mean similarity dendrograms to evaluate classifications. Journal of Agricultural, Biological, and Environmental Statistics 2:370-388.
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.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$counts), adj = -0.5,
expression(bold(delta)), cex=1.5 ) }
)
par(def.par)
## meandist
dune.md <- meandist(vegdist(dune), dune.env$Management)
dune.md
summary(dune.md)
plot(dune.md)Run the code above in your browser using DataLab