[R-sig-ME] accounting for overdispersion in binary GLMM in lme4

Ben Bolker bbolker at gmail.com
Wed May 14 04:30:33 CEST 2014

On 14-05-13 08:54 PM, Thomas Merkling wrote:
> Hi all,
> I have a large dataset (n= 893) of chick sex (0 or 1) and I am looking 
> at which variables can influence the probability of producing a male 
> versus a female.
> I had to put random effects for year (as I have data for different 
> years), fatherID and motherID (as I have many chicks for a same 
> individual and mother and father were not always with the same partner). 
> Surprisingly,  variance was zero (or almost depending on the models) for 
> all 3 random effects, but as I have seen that it can happen, so I kept 
> going.
> A model looked like that:
> mod = glmer (CodeSex ~ X *Y + Z + (1|Year) + (1|FatherID) + 
> (1|MotherID), family="binomial", data = sexratio)
> Using the dispersion_glmer function from the GLMM wiki website I 
> estimated overdispersion. The ratio was around 1.4, which is not very 
> high (but p-value highly significant, due to the large dataset?).
> I saw a lot of model alternatives when using count data, but the only 
> one I found for binary data seem to be adding an observation-level 
> random effect.

  Overdispersion is unidentifiable for binary data (unless there are
multiple observations with identical sets of predictors, in which case
the data can be aggregated into binomial data with N>1), so all of this
is more or less irrelevant/unnecessary ...

  Ben Bolker

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