meandist finds the mean within
and between block dissimilarities.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, kind = c("dendrogram", "histogram"), cluster = "average",
ylim, axes = TRUE, ...)vegdist for
options. This will be used if dat was not a dissimilarity
structure of a symmetmeandist result object.hclust
function for kind = "dendrogram".
Any hclust method can be used, but perhaps only
"average" and "single" maNA.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 the overall weighted mean of
within-group 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
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
$\delta$ 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
change-corrected within-group agreement
$A = 1 -\delta/E(\delta)$, where $E(\delta)$ is the expected
$\delta$ 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 within-cluster
dissimilarities (diagonal) and between-cluster dissimilarities
(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, CS (Van
Sickle and Hughes, 2000). CS is defined for dissimiliraties as
$\bar{B} - \bar{W}$, where $\bar{B}$ is the
mean between cluster dissimilarity and $\bar{W}$ 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 $\bar{W}$ and a good approximation
for CS. Function plot draws a dendrogram or a histogram of the
result matrix based on the within-group and between group
dissimilarities. The dendrogram is found with the method given in the
cluster argument using function hclust. The
terminal segments hang to within-cluster dissimilarity. If some of the
clusters are more heterogeneous than the combined class, the leaf
segment are reversed. The histograms are based on dissimilarites, but
ore otherwise similar to those of Van Sickle and Hughes (2000):
horizontal line is drawn at the level of mean between-cluster
dissimilarity and vertical lines connect within-cluster dissimilarities
to this line.
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.
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 <- with(dune.env, meandist(vegdist(dune), Management))
dune.md
summary(dune.md)
plot(dune.md)
plot(dune.md, kind="histogram")Run the code above in your browser using DataLab