The null hypothesis of absence of concordance is rejected. Thus, we can look for
groups of species, then proceed with the Kendall analysis of these groups
# k-means partitioning of species
spe.t.kmeans.casc <- cascadeKM(
spe.t,
inf.gr = 2,
sup.gr = 8,
iter = 100,
criterion = "calinski"
)
plot(spe.t.kmeans.casc, sortg = TRUE)
This result indicates that two groups may be a good choice. Avoid solutions with
groups containing a single species except when it is clear that this species belongs
to no other group. One group has 6 species and the other has 21. Three or four
groups would also be fine at this point of the analysis: all groups would have 3
species or more.
# The partition into 2 groups is found in column 1 of the
# object $partition
(clusters2 <- spe.t.kmeans.casc$partition[, 1])
Partitions into three or four groups:
(clusters3 <- spe.t.kmeans.casc$partition[, 2])
(clusters4 <- spe.t.kmeans.casc$partition[, 3])
We will now examine the division of the species in two groups. Let us run a
global Kendall W test on each group. This is done with a single call to the
kendall.global() function.
# Concordance analysis
(spe.kendall.global2 <- kendall.global(spe.hel, clusters2))
Look at the corrected permutational p-values. If all values are equal to or smaller
than 0.05, you can consider that all groups are globally significant, i.e. that on the
whole they contain species that are concordant; this does not mean that all species in
a globally significant group are concordant, only that at least some species are. If the
corrected p-values for some groups were not significant (it is not the case with this
example), it would indicate that these groups include non-concordant species and
should be subdivided into smaller groups. In other words, a partition into more than
2 groups would be in order.
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4 Cluster Analysis
groups of species, then proceed with the Kendall analysis of these groups
# k-means partitioning of species
spe.t.kmeans.casc <- cascadeKM(
spe.t,
inf.gr = 2,
sup.gr = 8,
iter = 100,
criterion = "calinski"
)
plot(spe.t.kmeans.casc, sortg = TRUE)
This result indicates that two groups may be a good choice. Avoid solutions with
groups containing a single species except when it is clear that this species belongs
to no other group. One group has 6 species and the other has 21. Three or four
groups would also be fine at this point of the analysis: all groups would have 3
species or more.
# The partition into 2 groups is found in column 1 of the
# object $partition
(clusters2 <- spe.t.kmeans.casc$partition[, 1])
Partitions into three or four groups:
(clusters3 <- spe.t.kmeans.casc$partition[, 2])
(clusters4 <- spe.t.kmeans.casc$partition[, 3])
We will now examine the division of the species in two groups. Let us run a
global Kendall W test on each group. This is done with a single call to the
kendall.global() function.
# Concordance analysis
(spe.kendall.global2 <- kendall.global(spe.hel, clusters2))
Look at the corrected permutational p-values. If all values are equal to or smaller
than 0.05, you can consider that all groups are globally significant, i.e. that on the
whole they contain species that are concordant; this does not mean that all species in
a globally significant group are concordant, only that at least some species are. If the
corrected p-values for some groups were not significant (it is not the case with this
example), it would indicate that these groups include non-concordant species and
should be subdivided into smaller groups. In other words, a partition into more than
2 groups would be in order.
114
4 Cluster Analysis