[R-sig-ME] glmer, split-plot design simple question

[Ben Bolker]

 <chico3 at ...> writes:

>

[snip]

> I have four luminaires randomly distributed. Two luminaires have light  
> on and two luminaires have no light. Below the luminaires I have two  
> treatments. Each treatment has four replicates that were randomly  
> distributed below the luminaires. Moreover, I have made all the  
> possible combinations of presence absence of light and treatments.
> 
> I want to check if there is a effect of each treatment and the  
> interactions between all the combinations.The response variable is a  
> proportion (number of specific specie/total number of species)
> 
> Treatment1<-as.factor(“Yes”,”No”)
> Treatment2<- as.factor(“Yes”,”No”)
> Light<- as.factor(“Yes”,”No”)
> Response<-cbind(number_of_specific_species, total_species)
> 
> I have made this model,
> 
>   model<-glmer(Response ~ Treatment1*Treatment2 + (1|Light), family=binomial)
> 
> However this doesn´t allow to see the effect of light or the  
> interaction between light and treatments. Moreover, I don´t know how  
> to include overdispersion, since glmer doesn´t allow quasi families  
> such as glm.
> 
> I know this is a simple question, but I greatly would appreciate some  
> clues on how to proceed.

I may be missing something here, but it doesn't make sense to me
to treat Light as a random effect (one criterion -- the levels "Light"
and "No light" aren't *exchangeable*, i.e. you couldn't switch
the factor labels without changing the meaning of the experiment).
I would say you are looking for something more like

glmer(Response ~ Treatment1*Treatment2*Light + (1|luminaire), family=binomial)

where the luminaires are labeled uniquely (e.g.
"Light1","Light2","Nolight1","Nolight2")

It sounds like this is a randomized block design (i.e. every level of
Treat1*Treat2 is present at each luminaire), so you could test the
interaction between Treat1*Treat2 and luminaire via
(Treat1*Treat2|luminaire) instead of (1|luminaire) (see e.g.
Schielzeth 2009), although you may find that this leads to estimates
of zero variance (overfitting the data).