ordispider(ele.rda.out, ele.fac,
scaling = 1,
label = TRUE,
col = "blue"
)
spe.sc1
display = "species")
arrows(0, 0,
spe.sc1[, 1] * 0.3,
spe.sc1[, 2] * 0.3,
length = 0.1,
angle = 10,
col = "red"
)
text(
spe.sc1[, 1] * 0.3,
spe.sc1[, 2] * 0.3,
labels = rownames(spe.sc1),
pos = 4,
cex = 0.8,
col = "red"
)
Hints To convince yourself that this procedure is the exact equivalent of an ANOVA,
apply it to species 1 only, and then run a traditional ANOVA on species 1 with
factors ele.fac and pH.fac, and compare the F-values. The probabilities may
differ slightly since they are permutational in RDA.
In the permutational tests of each main effect, the argument strata restricts the
permutations within the levels of the other factor. This ensures that the proper H 0
is produced by the permutation scheme. Note that the use of blocks allows one to
apply these analyses to nested (e.g. split-plot) designs.
If you want to create a matrix of Helmert contrasts with the crossed main factors
only, without the interaction terms, replace '*' by '+' in the formula: …~ele.fac
+ pH.fac… Examine the documentation files of functions model.matrix(),
contrasts() and contr.helmert().
In the triplot section, observe how we use function ordispider() to relate the
“wa” site scores to the centroids of the factor levels.
Figure 6.6 represents the “wa” scores of the sites (to show their dispersion) related
to the centroids of the factor levels by means of straight lines, in scaling 1. The
species arrows have been added (in red) to expand the interpretation.
Figure 6.6 cleanly shows the relationships of selected groups of species with
elevation. This factor can be seen as a proxy for several important environmental
variables, so that this analysis is quite informative. The figure also allows one to
242
6 Canonical Ordination
scaling = 1,
label = TRUE,
col = "blue"
)
spe.sc1
display = "species")
arrows(0, 0,
spe.sc1[, 1] * 0.3,
spe.sc1[, 2] * 0.3,
length = 0.1,
angle = 10,
col = "red"
)
text(
spe.sc1[, 1] * 0.3,
spe.sc1[, 2] * 0.3,
labels = rownames(spe.sc1),
pos = 4,
cex = 0.8,
col = "red"
)
Hints To convince yourself that this procedure is the exact equivalent of an ANOVA,
apply it to species 1 only, and then run a traditional ANOVA on species 1 with
factors ele.fac and pH.fac, and compare the F-values. The probabilities may
differ slightly since they are permutational in RDA.
In the permutational tests of each main effect, the argument strata restricts the
permutations within the levels of the other factor. This ensures that the proper H 0
is produced by the permutation scheme. Note that the use of blocks allows one to
apply these analyses to nested (e.g. split-plot) designs.
If you want to create a matrix of Helmert contrasts with the crossed main factors
only, without the interaction terms, replace '*' by '+' in the formula: …~ele.fac
+ pH.fac… Examine the documentation files of functions model.matrix(),
contrasts() and contr.helmert().
In the triplot section, observe how we use function ordispider() to relate the
“wa” site scores to the centroids of the factor levels.
Figure 6.6 represents the “wa” scores of the sites (to show their dispersion) related
to the centroids of the factor levels by means of straight lines, in scaling 1. The
species arrows have been added (in red) to expand the interpretation.
Figure 6.6 cleanly shows the relationships of selected groups of species with
elevation. This factor can be seen as a proxy for several important environmental
variables, so that this analysis is quite informative. The figure also allows one to
242
6 Canonical Ordination