# Variation partitioning
(spe.part <- varpart(spe.hel, envchem.pars, envtopo.pars))
plot(spe.part,
digits = 2,
bg = c("red", "blue"),
Xnames = c("Chemistry", "Physiography"),
id.size = 0.7
)
# Tests of all testable fractions
# Test of fraction [a+b]
anova(rda(spe.hel, envchem.pars), permutations = how(nperm = 999))
# Test of fraction [b+c]
anova(rda(spe.hel, envtopo.pars), permutations = how(nperm = 999))
# Test of fraction [a+b+c]
env.pars <- cbind(envchem.pars, envtopo.pars)
anova(rda(spe.hel, env.pars), permutations = how(nperm = 999))
# Test of fraction [a]
anova(rda(spe.hel, envchem.pars, envtopo.pars),
permutations = how(nperm = 999)
)
# Test of fraction [c]
anova(rda(spe.hel, envtopo.pars, envchem.pars),
permutations = how(nperm = 999)
)
Are any of these components non-significant?
As expected, forward-selecting the explanatory variables independently in each
subset (chemistry and physiography) does nothing to prevent inter-set correlations;
some of the variables retained in each set are correlated with those of the other set.
Therefore, fraction [b] remains important. Beware: conducting variable selection on
the union of the two explanatory data sets would make fraction [b] very small or
empty because pairs or groups of collinear variables would be less likely to be
retained in the model. In this type of analysis, we do not want to eliminate the
common fraction, we want to estimate its magnitude and interpret it. If one wants to
estimate how much of the variation of Y is explained jointly by two or more
explanatory data sets (usually because they represent different categories of constraints), it is important to carry out forward selection separately on the sets of
explanatory variables.
In this example, the two independent forward selections run above have retained
the same variables as when the whole set had been submitted to forward selection
(i.e., ele, oxy, bod) plus variables slo and nit. The latter is strongly
correlated to ele (r ¼ À0.75). This means that in the RDA with the chemical
variables, nit has explained some of the same structures as ele was explaining in
236
6 Canonical Ordination
(spe.part <- varpart(spe.hel, envchem.pars, envtopo.pars))
plot(spe.part,
digits = 2,
bg = c("red", "blue"),
Xnames = c("Chemistry", "Physiography"),
id.size = 0.7
)
# Tests of all testable fractions
# Test of fraction [a+b]
anova(rda(spe.hel, envchem.pars), permutations = how(nperm = 999))
# Test of fraction [b+c]
anova(rda(spe.hel, envtopo.pars), permutations = how(nperm = 999))
# Test of fraction [a+b+c]
env.pars <- cbind(envchem.pars, envtopo.pars)
anova(rda(spe.hel, env.pars), permutations = how(nperm = 999))
# Test of fraction [a]
anova(rda(spe.hel, envchem.pars, envtopo.pars),
permutations = how(nperm = 999)
)
# Test of fraction [c]
anova(rda(spe.hel, envtopo.pars, envchem.pars),
permutations = how(nperm = 999)
)
Are any of these components non-significant?
As expected, forward-selecting the explanatory variables independently in each
subset (chemistry and physiography) does nothing to prevent inter-set correlations;
some of the variables retained in each set are correlated with those of the other set.
Therefore, fraction [b] remains important. Beware: conducting variable selection on
the union of the two explanatory data sets would make fraction [b] very small or
empty because pairs or groups of collinear variables would be less likely to be
retained in the model. In this type of analysis, we do not want to eliminate the
common fraction, we want to estimate its magnitude and interpret it. If one wants to
estimate how much of the variation of Y is explained jointly by two or more
explanatory data sets (usually because they represent different categories of constraints), it is important to carry out forward selection separately on the sets of
explanatory variables.
In this example, the two independent forward selections run above have retained
the same variables as when the whole set had been submitted to forward selection
(i.e., ele, oxy, bod) plus variables slo and nit. The latter is strongly
correlated to ele (r ¼ À0.75). This means that in the RDA with the chemical
variables, nit has explained some of the same structures as ele was explaining in
236
6 Canonical Ordination