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Question on overdispersion

David Jansen 
Dear Jarrod,

recently you suggested that to overcome overdispersion in a binomial distribution by fitting a observation-level random effect.
I was wondering if this method has been described anywhere so I can put a reference in my report.

Thanks a lot,
Greetings David Jansen



Hi Thierry + nameless,

It is not necessary to expand the binomial into Bernoulli trials (nor
advisable if n and/or the binomial size are large). You can just fit
observation-level random effects:

dataset$resid<-as.factor(1:dim(dataset)[1])

fit3<- glmer(cbind(male_chick_no, female_chick_no) ~ 1+(1|FemaleID)+
(1|resid), data = dataset, family = binomial)

gives the same answer as fit2

Cheers,

Jarrod