I am designing a large-scale sampling effort aimed primarily at determining
the influence of rainfall on nitrogen isotope (*15N*) values in trees.  My
system is a precipitation gradient across a tropical rainforest and I am
attempting to plan carefully before heading out into the field for what will
amount to a great effort.  As the ecological world is not a perfect
experimental system, soil fertility is found to vary as widely within
different rainfall regimes as it does across the entire gradient.  This may
greatly confound interpretations.  Also, tree species turnover across the
gradient with no single species spanning the entire range (partially crossed
combinations will be possible however).  I am therefore thinking of
designing my sampling strategy to account for variation in my response
brought on by these covariates.

I believe this would be described as a nested or hierarchical mixed effects
model (with partially crossed species) looking something like this:

fit 1 <- lmer(15N ~  rainfall + ( 1 | fertility/plot/species )

1) Am I correct that internally this model has the random effects of: ( 1 |
fertility ) + ( 1 | fertility:plot ) + ( 1 | fertility:plot:species )?  And
can *fertility* alternatively be fixed yet still have random effects nested
within it?

2) If *rainfall* is categorically binned into low, medium, and high what
will I gain or lose versus if I treat it as continuous (say: 1900, 2400, and
3600 mm)?  This could also go for *fertility* which could be represented as
either artificially demarcated categories (low, medium, high) or as say a
continuous principle component score to reduce dimensionality yet maintain
continuity.

3) Related to this, do I need 5 levels to accurately fit a random variable
(as I've read elsewhere on this listserve) or is 3 O.K.?

4) Also, if I am missing all of the 3 (or 5) categories of soil fertility
for each rainfall level, will this doom the model fit?

5) I expect to have 10 responses measured from each plot but only single, or
possibly two, unique combinations.  Is it crazy to not replicate at the
*plot* level within each "fertility*-*rainfall* combination ?

If it helps the discussion, I imagine the data will look something like this
in R:

> imaginary data (15Npatterns)
> str (15Npatterns)

'data.frame':        __ obs. of 5 variables:
$ 15N          :  num  1.00  1.52  -1.13   3.47   5.12   0.87   …
$  rainfall     :  Factor w/ 3 levels "A", "B", "C":        1 1 2 2 3 3
$  fertility     :  Factor w/ 3 levels "l", "m", "h":        ? ? ? ?
$  plot          :  Factor w/ 3 levels "A:l", "B:m", "C:h" :    ? ? ? ?
$  sample    :  Nominal :     Anacardium spp., Brosmium sp., etc.

> summary(15Npatterns)
rainfall    fertility        plot        sample
A    : 2     l                 A:l          A:l:sp      : 10
B    : 2    m               B:m        B:m:sp    : 10
C    : 2    h                C:h         C:h:sp     : 10


Thanks in advance and I appreciate any advice.

-- 
Jordan

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