# [R-sig-ME] random effects specification

Julie Marsh marshj02 at student.uwa.edu.au
Mon May 5 04:12:59 CEST 2008

```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
>
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> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>

```