Ben,
There are a few old threads that you might find useful, search the 
following:

random effect variance per treatment group in lmer
heteroscedastic model in lme4
Stratifying level-1 variance with lmer()
Different random effects variances for outcomes and groups
Behavior of coef() for lmer() model w/ level-2 variance stratified

I think in one of them I provided a summary of some of the issues but I 
can't seem to find it at the moment.

Cheers,
David





On 02/14/2011 02:53 PM, Ben Bolker wrote:
>    This is a question that's been bothering me for a while.  The answer
> might be "read sections 4.2.2 and 4.2.3 of Pinheiro and Bates 2000
> again, more carefully", but if anyone has done this before I wouldn't
> mind some hints ...
>
>    Consider a simplified version of the previous poster's example.
> Suppose I have a randomized block design where T treatments are done for
> each of N individuals within each of S species. My basic model for this
> would be
>
>    response~treatment+(treatment|species/indiv)
>
> (or fixed=response~treatment, random=~treatment|species/indiv in lme)
>
> which would give me random effects
>
> 1|species
> 1|indiv:species
> treatment|species
> treatment|indiv:species
>
> (and correlations between intercept and treatment effects at species and
> indiv:species level).
>
>    Suppose now that I think the *variance* among individuals varies among
> species.  As far as I can tell, lme/lmer assume that this variance is
> constant across species.  If I wanted variance across *observations*
> (i.e. residual variance) to vary across species I could do it via
> something like weights=varIdent(~species), but this only works for
> residual variance.
>
>    I suspect I could work out some way to do this with MCMCglmm, and I
> don't have an immediate need for it, but I thought I would ask ...
>
>   thanks
>      Ben Bolker
>
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-- 
David Afshartous, Ph.D.
Research Associate Professor
School of Medicine
Department of Biostatistics
Vanderbilt University


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