random effects specification

Dear Sebastian, Sounds as if you have received great advice already.
Just a short note - I believe you are missing the fixed-effect
intercept in your model which I have denoted as simply "B" in your
notation below.  This is often denoted as Beta0 or B0 in textbooks
(sorry no subscripts or greek letters printing in this email!).

y_{ijk} = B + B_j + B_k + B_{jk} + b_i + e_{ijk} i=1,...,20; j=A,B;
k=a,b,c

kindest regards, julie.

Quoting "Sebastian P. Luque"
<spluque at gmail.com>:

Hi again,

I've made further explorations into lmer, toying with the example I
showed earlier:

---<---------------cut here---------------start-------------->---
set.seed(1000) rCom <- rnorm(2, mean=5, sd=0.5) rTr <- rep(rCom /
1.1, 2) nbase <- rnorm(60, 10, 0.1)

## 20 individuals; 10 in community "A" and 10 in "B", each receiving
3 ## different treatments once.  dta <-
within(expand.grid(community=LETTERS[1:2], treatment=letters[1:3],
id=1:10), { id[community == "B"] <- id[community == "B"] + 10 id <-
as.factor(id) n <- rCom[as.numeric(community)] +
rTr[as.numeric(treatment)] + nbase }) dta <- dta[order(dta$id,
dta$community, dta$treatment), ]

## Simulate an interaction dta$n[dta$community == "A"] <-
rev(dta$n[dta$community == "A"]) ## Have a look xyplot(n ~ treatment
| community, data=dta, groups=id, type="b", pch=19, cex=0.3)

## We test for community (A, B) and treatment (a, b, c) fixed
effects, ## their interactions, and use random effects for subject
(1:20).  Am I ## writing this correctly?  ## ## y_{ijk} = B_j + B_k +
B_{jk} + b_i + e_{ijk} i=1,...,20; j=A,B; k=a,b,c n.lmer1 <- lmer(n ~
community * treatment + (1 | id), dta) ---<---------------cut
here---------------end---------------->---

I'm a bit confused whether I'm describing the model being fit
correctly (not the lmer call, but the model description in the
comment above), and how it could be described in matrix form.  I
think this type of exercises would help me grasp the syntax
conventions better.

Another issue is that the lmer call results in a warning:

---<---------------cut here---------------start-------------->---
Warning message: In .local(x, ..., value) : Estimated variance for
factor ?id? is effectively zero ---<---------------cut
here---------------end---------------->---

which I presume is due to the fact that the data are unreplicated,
i.e. individuals get each treatment only once.  Are there any gotchas
in the interpretation of the results after this warning?

Thanks once again!

-- Seb