# Preparation of data (transformations to make variable
# distributions approximately symmetrical)
envchem2 <- envchem
envchem2$pho <- log(envchem$pho)
envchem2$nit <- sqrt(envchem$nit)
envchem2$amm <- log1p(envchem$amm)
envchem2$bod <- log(envchem$bod)
envtopo2 <- envtopo
envtopo2$ele <- log(envtopo$ele)
envtopo2$slo <- log(envtopo$slo)
envtopo2$dis <- sqrt(envtopo$dis)
# CCorA (on standardized variables)
chem.topo.ccora
stand.X = TRUE,
permutations = how(nperm = 999))
chem.topo.ccora
biplot(chem.topo.ccora, plot.type = "biplot")
Hint The biplot(){vegan} function used here recognizes the structure of a CCorA
object. If you type biplot(chem.topo.ccora) without adding the argument
plot.type = "biplot", you obtain separate plots of sites and variables,
i.e., four graphs in a single frame; easier to compare for large data sets.
The result shows that there is a significant relationship between the two matrices
(permutational probability ¼ 0.001). Pillai’s trace statistic is the sum of the squared
canonical correlations. The canonical correlations are high on the first two axes. The
RDA R
2 and adjusted R
2 are not part of the CCorA computations strictly speaking;
the two RDAs are computed separately for information. This information is useful to
assess whether the canonical axes are likely to express a substantial amount of
variation (which is the case here), since canonical correlations may be large even
when the common variation is small with respect to the total variation of the two
data sets.
In Fig. 6.16, the left-hand biplot shows the standardized chemical variables and
the objects projected in their space. The right-hand biplot shows the standardized
physiographic variables and objects in their space. Note that the two spaces are
“aligned” with respect to one another, i.e. the canonical axes show the same trends
expressed by the two sets of variables. The positions of the sites in the two biplots are
related, although not similar. The structures displayed are the result of linear
combinations of variables in each of the biplots. The pair of biplots expresses the
fact that oxygenated waters (oxy) are related to high elevation (ele) and steep
276
6 Canonical Ordination
# distributions approximately symmetrical)
envchem2 <- envchem
envchem2$pho <- log(envchem$pho)
envchem2$nit <- sqrt(envchem$nit)
envchem2$amm <- log1p(envchem$amm)
envchem2$bod <- log(envchem$bod)
envtopo2 <- envtopo
envtopo2$ele <- log(envtopo$ele)
envtopo2$slo <- log(envtopo$slo)
envtopo2$dis <- sqrt(envtopo$dis)
# CCorA (on standardized variables)
chem.topo.ccora
stand.X = TRUE,
permutations = how(nperm = 999))
chem.topo.ccora
biplot(chem.topo.ccora, plot.type = "biplot")
Hint The biplot(){vegan} function used here recognizes the structure of a CCorA
object. If you type biplot(chem.topo.ccora) without adding the argument
plot.type = "biplot", you obtain separate plots of sites and variables,
i.e., four graphs in a single frame; easier to compare for large data sets.
The result shows that there is a significant relationship between the two matrices
(permutational probability ¼ 0.001). Pillai’s trace statistic is the sum of the squared
canonical correlations. The canonical correlations are high on the first two axes. The
RDA R
2 and adjusted R
2 are not part of the CCorA computations strictly speaking;
the two RDAs are computed separately for information. This information is useful to
assess whether the canonical axes are likely to express a substantial amount of
variation (which is the case here), since canonical correlations may be large even
when the common variation is small with respect to the total variation of the two
data sets.
In Fig. 6.16, the left-hand biplot shows the standardized chemical variables and
the objects projected in their space. The right-hand biplot shows the standardized
physiographic variables and objects in their space. Note that the two spaces are
“aligned” with respect to one another, i.e. the canonical axes show the same trends
expressed by the two sets of variables. The positions of the sites in the two biplots are
related, although not similar. The structures displayed are the result of linear
combinations of variables in each of the biplots. The pair of biplots expresses the
fact that oxygenated waters (oxy) are related to high elevation (ele) and steep
276
6 Canonical Ordination