Dear r-sig-mixed-models List,

I've been digging through the r-help archive and various books in search of
an answer to my query. I have been thus far unsuccessful. I am not new to R,
but have primarily focused on multivariate non parametric analyses in the
past; my experience with lmer has been confined to the last few weeks. The
model formulas I have written work and I have some idea of which are
accurate/best based on AIC scores, but I would very much appreciate an
informed opinion on my syntax.

I am performing an ecological study of stream health using %EPT (An
aggregate relative abundance variable for invertebrates) as my response
variable. I am interested in how invertebrate counts vary between different
watershed types (forested, cultivated, developed, grassland) and reach types
(forested, non forested). There are a total of 12 streams, 12 watersheds and
24 reaches. The wshed factor is unbalanced.

Data structure:
> str(ept)
'data.frame':    72 obs. of  4 variables:
 $ wshed  : Factor w/ 4 levels "c","d","f","g": 1 1 1 1 1 1 1 1 1 1 ...
 $ stream : Factor w/ 12 levels "BA","D1","D2",..: 4 4 4 6 6 6 10 10 10 4
...
 $ riparia: Factor w/ 2 levels "F","N": 1 1 1 1 1 1 1 1 1 2 ...
 $ ept    : num  0.318 0.156 0.194 0.146 0.158 ...

stream is the only random variable and it is nested (not implicitly) in
wshed. My standard statistical model is as follows:
ept(ijkl) = ì + wshedi  + stream(i)j + ripariak + wshed*ripariaik +
stream*riparia(i)jk + å(ijk)l

The best option I have come up with thus far is:
>model<-lmer(ept ~ wshed + riparia + wshed:riparia + (1| wshed/stream) + (1|
stream:riparia), data=ept, family="gaussian")
or alternatively:
>model<-lmer(ept ~ wshed*riparia + (1| wshed/stream) + (1| stream:riparia),
data=ept, family="gaussian")

Question: Am I specifying the random terms and nesting structure correctly?

Secondarily: I have read a few times that "wshed/stream" is interchangeable
with  "wshed:stream" which is a meaningless interaction. Also I've seen that
random effects are specified as (a|b) where a is a covariate and b is a
grouping factor. Does having 1 as a covariate simply specifying an intercept
of 1? What is the purpose of placing a factor in the place of 1 as a
covariate? OR is there a nice complete summary tutorial that I've missed.


I'm looking forward to hearing any comments.

Thank you,
-- 
Colin Wahl
Department of Biology
Western Washington University
Bellingham, WA 98225
ph: 360-391-9881

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