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mantel within mantel? multidimensional variance

2 messages · Mgr. Martin Weiser, Bob OHara

Original
Mgr. Martin Weiser
# 
Dear friends,

I need to quantify variance within variance, and what is worse, say if
it is non-random.
This is the setup: in the experiment, there were 2 (partly correlated)
treatments, each of six levels (but theoretically of infinite levels,
so I treated them as continuous).
Different species responded to them, and we measured various traits
("endotraits").

We used R2 from the per-species redundancy analyses (RDA) as a
reaction norm: higher R2, more the species responds to the treatment
(so traits were used as "species" in the community ecology jargon). We
have twice as much RDAs as there were species (because of 2
treatments).

Next, we correlated these R2 (reaction norms) with some other traits
per species ("exotraits"). As there were 2 correlated treatments (lets
say irrigation and fertilisation), and we used the same reaction norms
for correlation with different exotraits, the correlations were
obviously non independent. To overcome this, we run Mantel test
(matrix1= species x reaction norms to treatment, matrix2=species x
exotraits).

Next, we are interested in "endotraits" x "exotraits" correlation. For
this, we used endotrait scores from the per-species RDAs on the
treatment axis (constraining variable). Correlations are
non-independent again, so we wanted an overall test. And here comes
the problem: results of Mantel tests (matrix1=species x endotrait
scores, matrix2=species x exotraits) are suprisingly weak. Some single
correlations of endotrait scores x exotraits seem to be pretty afar
from random, but the overall mantel...

I think this is because single endotrait can not show better
correlation than the overall reaction norm, which is based on them, so
something like (pval of this mantel)*(1-pval of the correlation of
reaction norm with exotraits) may be desirable for the overall test,
but I simply do not know.

Any advice?

Best,
Martin Weiser
Bob OHara
# 
Do you need to run Mantel tests at all? I don't see that you have 
measured any distances, as such, so I think you can do at leat as well 
by using standard [genrealized] linear [mixed] models.

I'm not sure I understand everything, but it sounds like you run an 
experiment with 2 treatments, and N species, and you measure T traits. 
So, for each trait you could have a model

y_t ~ (Treat1 + Treat2)*Species
(you could run this separately for each species, if that makes things 
easier)

and size of the Treat1:Species effect tells you how the species responds 
to the treatment (if you want a measure over all traits, a PCA on the 
coefficients should suffice).

It sounds like you are then asking how these reactions, i.e. the 
Treat1:Species effects are related to traits which are constant within a 
species, i.e. a Treat1:Trait effect.

So, for each y_t you could run a model

y_t ~ (Treat1 + Treat2)*(Trait+Species)
(or even make Species a random effect)

So, now I think you just want the Treat1:Trait effects. if the Trait's 
are discrete classes, then you can (again) run a PCA on the effects, to 
visualise the effects.

If you want to analyse all of the y_t's together, it gets a bit more 
complicated, but in principle it's the same, except you have a 
MANOVA-like structure. I think you could use a Seemingly Unrelated 
Regression approach.

Bob
On 06/08/2014 05:56 PM, Mgr. Martin Weiser wrote: