[R-sig-ME] random effects specification

[Ken Beath]

On 05/04/2008, at 12:05 AM, Sebastian P. Luque wrote:
> On Fri, 4 Apr 2008 07:17:36 -0500,
> "Douglas Bates" <bates at stat.wisc.edu> wrote:
>
> [...]
>
>> I'm not sure that I understand what you mean by "treatment being
>> nested within community".  Does this mean that there are really 8
>> different treatments because treatment 1 in community A is different
>> from treatment 1 in community B?  If so, then it would make sense to
>> me to simply create a new factor that is the interaction of treatment
>> and community.
>
> I was not employing the term "nested" properly.  The number of levels
> for both community and treatment are 2 and 4, respectively, just as in
> the example.  The same 4 treatments were used in both communties, so  
> in
> fact, treatment is crossed with community, not nested.  However,
> subjects are nested within communities because each subject belongs to
> one community only, yet received all 4 treatments.  Sorry for this
> confusion.
>

Once they are considered fixed effects, concepts of crossing and  
nesting are irrelevant. They are simply covariates. So a model of the  
form n ~ treatment + community +(1|id) or if the treatment effect is  
allowed to vary between communities n ~ treatment *community +(1|id)  
is appropriate. The main problem is your subject id are not unique.  
You will need to define a new id. The easiest way is to add a  
different large number to id depending on community.


>
>> Perhaps I am approaching the community factor incorrectly.  In your
>> data there are two communities so, even if it would be reasonable to
>> model community effects as random effects, that would be difficult.
>> With only two levels I think it is best modeled as a fixed effect,
>> which would mean that questions about treatment and community are
>> related to the fixed effects.
>
> Could you please show a formula for the case where each individual is
> seen at both communities (community and treatment still being fixed)?
> This would help me understand the syntax better.
>

Same model as previous, provided a subject only receives a treatment  
once. If a subject receives the same treatment more than once then  
there needs to be a random effect that models the correlation between  
repeated measurements of the same treatment, so the model is  
y~treatment+community+(1|id/treatment) One problem that may have  
occurred in your original attempts is that id and treatment need to be  
factors.

Ken

> Thank you so much for your help.
>
>
> -- 
> Seb
>
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