the physiography RDA. Removing nit from the chemical variables and running the
partitioning again changes the result:
## 3. Variation partitioning without the 'nit' variable
envchem.pars2 <- envchem[, c(6, 7)]
(spe.part2 <- varpart(spe.hel, envchem.pars2, envtopo.pars))
plot(spe.part2, digits = 2)
This last partitioning has been run to demonstrate the effect of correlation
between the explanatory variables of different sets. However, one generally applies
variation partitioning to assess the magnitude of the various fractions, including the
common ones. If the aim is to minimize the correlation among variables, other
approaches are preferable (examination of the VIFs, global forward selection).
With this warning in mind, we can examine what the comparison between the two
latter partitionings tells us. Interestingly enough, the overall amount of variation
explained is about the same (0.595 instead of 0.590). The [b] fraction has dropped
from 0.196 to 0.088 and the fraction (elevation + slope) explained uniquely by
physiography has absorbed the difference, rising from 0.142 to 0.249. This does not
mean that elevation is a better causal candidate than nitrates to explain fish communities. Comparison of the two analyses rather indicates that nitrate content is related
to elevation, just as the fish communities are, and that the interpretation of variables
elevation and nitrates must be done with caution since their causal link to the fish
communities cannot be untangled. On the other hand, elevation is certainly related to
other, unmeasured environmental variables that have an effect on the communities,
making it a good proxy for them.
The comparisons above tell us that:
1. Forward selection provides a parsimonious solution without sacrificing real
explanatory power: the R
2
adj of the three partitionings are approximately equal.
2. The common fractions, which are one of the reasons why partitioning is computed, must be interpreted with caution, even when the variables responsible for
them are biologically legitimate.
3. Forward-selecting all explanatory variables before attributing the remaining ones
to subsets is in contradiction with the aim of variation partitioning, except to help
identify the magnitude of the effect of some variables responsible for the common
fractions.
4. Forward selection and variation partitioning are powerful statistical tools. As such
they can help support sound ecological reasoning but they cannot replace it.
Final note about the [b] fraction This common fraction should never be mistaken
for an interaction term in the analysis of variance sense. One more time, let us stress
that the common fractions arise because explanatory variables in different sets are
correlated. In contrast, in a replicated two-way ANOVA, an interaction measures the
influence of the levels of one factor on the effect of the other factor on the response
6.3 Redundancy Analysis (RDA)
237
partitioning again changes the result:
## 3. Variation partitioning without the 'nit' variable
envchem.pars2 <- envchem[, c(6, 7)]
(spe.part2 <- varpart(spe.hel, envchem.pars2, envtopo.pars))
plot(spe.part2, digits = 2)
This last partitioning has been run to demonstrate the effect of correlation
between the explanatory variables of different sets. However, one generally applies
variation partitioning to assess the magnitude of the various fractions, including the
common ones. If the aim is to minimize the correlation among variables, other
approaches are preferable (examination of the VIFs, global forward selection).
With this warning in mind, we can examine what the comparison between the two
latter partitionings tells us. Interestingly enough, the overall amount of variation
explained is about the same (0.595 instead of 0.590). The [b] fraction has dropped
from 0.196 to 0.088 and the fraction (elevation + slope) explained uniquely by
physiography has absorbed the difference, rising from 0.142 to 0.249. This does not
mean that elevation is a better causal candidate than nitrates to explain fish communities. Comparison of the two analyses rather indicates that nitrate content is related
to elevation, just as the fish communities are, and that the interpretation of variables
elevation and nitrates must be done with caution since their causal link to the fish
communities cannot be untangled. On the other hand, elevation is certainly related to
other, unmeasured environmental variables that have an effect on the communities,
making it a good proxy for them.
The comparisons above tell us that:
1. Forward selection provides a parsimonious solution without sacrificing real
explanatory power: the R
2
adj of the three partitionings are approximately equal.
2. The common fractions, which are one of the reasons why partitioning is computed, must be interpreted with caution, even when the variables responsible for
them are biologically legitimate.
3. Forward-selecting all explanatory variables before attributing the remaining ones
to subsets is in contradiction with the aim of variation partitioning, except to help
identify the magnitude of the effect of some variables responsible for the common
fractions.
4. Forward selection and variation partitioning are powerful statistical tools. As such
they can help support sound ecological reasoning but they cannot replace it.
Final note about the [b] fraction This common fraction should never be mistaken
for an interaction term in the analysis of variance sense. One more time, let us stress
that the common fractions arise because explanatory variables in different sets are
correlated. In contrast, in a replicated two-way ANOVA, an interaction measures the
influence of the levels of one factor on the effect of the other factor on the response
6.3 Redundancy Analysis (RDA)
237