[ORDNEWS:1839] RDA and significance, strength, and independence of an environmental variable

Petr Šmilauer

2014-03-08 20:25:32 UTC

Dear Dr. Doriedson Ferreira Gomes,
from your description it seems that you might be following some specific
protocol that I am not aware of, so some of my comments might not be
fully relevant then. I insert them between your original text lines.

Good morning! I work with paleolimnology and I need to determine the significance, strength and independence of an
environmental variable (water depth) as a determinant of the diatom assemblage in a Brazilian lake. I Will do that
using Canoco 4.5 and I would like to know if the approach I adopted is correct. I have doubts where I can get these
informations; specifically, in what time of the analytical process I can get the information I need.
To test the significance of my explanatory variables I will use a RDA with an "Automatic forward selection using a
Monte Carlo Permutation Test" to select significant environmental variables in my data set. From 9 variables I have, 4
were significant to explain the variability in species data. Hitherto, it's all right!

I am not so sure :-) If you base your decision about significant predictors on the
automated forward selection without at least checking the independent (marginal)
effects, you might miss important information. If, say, variables A and B explain,
respectively, 43 and 41% of your diatom assemblage data, and they are strongly
correlated (positively or negatively), it is likely that the stepwise selection picks up
variable A and then the variable B drops in the forward selection list and becomes
non-significant. Another issue is that the Type I error becomes inflated on
repeated testing using the same response data, so an adjustment of the obtained
P values might be appropriate (see Blanchet et al. 2008 in Ecology; BTW Canoco 5
implements the recommendations presented there).

After that, I will perform a RDA with only water depth as environmental variables; I will do the same for the others
significant variables. From these RDAs I will take the constrained RDA λ1 (marginal effect, correct?);

With only one explanatory ("environmental") variable in your RDA, only first
axis is constrained, so the first eigenvalue represents the variation explained by
it; and yes, this is its simple (marginal) effect.

the λ1/λ2 (to obtain the relative explanatory strength, correct?);

I have never seen such approach. "relative" to what? The second axis of your
RDA is the first unconstrained axis, but there are many of them. I am not sure
what you try to achieve here: perhaps it would be better to compare with the
first axis of PCA, which represents the maximum you can explain in your
diatom data with a single, but ideal predictor.

and the marginal variance % (in CCA this is calculated by dividing the eigenvalue
of axis-1 divided by the total inertia (the sum of all canonical axes);

The total inertia is total variation in your response ("species") data. Certainly,
sum of all canonical axes is a different thing (the part of the total variation,
that can be explained by your chosen explanatory ("environmental") variables.

in RDA, the λ1 and the sum of all canonical eigenvalues in my analysis is the same).

Not surprising at all, see above. Sum of all canonical eigenvalues is the
sum of eigenvalues of constrained axes and you have just one with
a single quantitative explanatory variable. I believe, however,
that you want to compare with the total variance and that is set to 1.0
in linear methods (PCA,RDA - unless you use a partial analysis).
So, the % of explained variation is the eigenvalue multiplied by 100.

Therefore, in RDA the marginal effect and the marginal variance
are the same.

Does not make any sense to me, but I do not know, what you
mean by "marginal variance".

When I perform a RDA with only water depth as environmental variable
this is a partial constrained ordination, correct?

No. This is a constrained ordination with one constraint (the water depth).
For a partial ordination you need covariates (or covariables, as
Canoco 4.5 calls them).

Where I can get (1) the total and (2) the unique (independent)
variation accounted for by each variable?

If (1) means "the total variation accounted for by a variable",
then this is the same as the "independent effect of that variable".
But many authors use the word "unique" for a partial (not independent)
effect, i.e. when asking how much is a variable able to explain
in addition to other ones (used as covariates).
The independent effects can be obtained, after you have run
an "automatic forward selection", by clicking the "FS summary"
button. It shows in the upper part of the dialog then (Marginal Effects).
But it is shown without tests of significance (unlike the report of
Canoco 5, when an analysis is run with the "Summarize effects
of expl. variables" option).

Thanks for your attention. Sorry for the basic questions. My best regards,

With my best regards

Petr Smilauer
Ceske Budejovice, CZ
---------------------------------------------------------------
International course Multivariate Analysis of Ecological Data
(February 2014): http://regent.jcu.cz
Book by course lecturers:
"Multivariate analysis of ecological data using Canoco 5"
at <http://www.cambridge.org/9781107694408>
Canoco 5 http://www.canoco5.com and http://www.canoco.com

--
***********************************************
Doriedson Ferreira Gomes
Professor Adjunto (Fitoplâncton e Limnologia)
Laboratório de Taxonomia, Ecologia e Paleoecologia de Ambientes Aquáticos - ECOPALEO
Dept. de Botânica - Instituto de Biologia - Universidade Federal da Bahia