[R-sig-ME] overdispersion estimation in a binomial GLMM

[Ben Bolker]

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On 01/21/2011 11:11 AM, Thomas Merkling wrote:
> Thanks to Robert and Ben for their precious answers !
> 
> I tried the dispersion function it works and gives me a 1.244403 value.
> As it is not really bigger than 1, should I treat my model as
> overdispersed ?

  Perhaps not. (How many observations?)

> Moreover I tried to fit an observation level random effect as suggested
> by Ben Bolker, but it gives me an error message !
> 
> 
> dispersion_glmer(model)#  1.244403
> baba$obs <- 1:nrow(baba)
> 
>  model_OD <-
> + glmer(propNb~SexA*SexB*AgeA+(1|Nest)+(1|obs),data=baba,family="binomial")
> Number of levels of a grouping factor for the random effects
> is *equal* to n, the number of observations
> 
> 

  That is a 'message' (not even a 'warning'), rather than an error.
Doug Bates was initially quite suspicious of this approach (adding a
random effect for every observation), which makes little sense in the
LMM case (where it would be confounded with the residual error).  Maybe
I will prevail upon him to see if we can drop the message since it makes
people worry unnecessarily ...

  If you wanted a crude test, you could compare the log-likelihoods of
your model with and without the overdispersion term (via anova()).  The
p-value of the likelihood ratio test computed in this way is
approximately double what it should be (because the null value of the
variance parameter (zero) is on the boundary of its feasible space) but
it should give you an approximate idea ...

> So what is the problem with this ?
> 
> Thanks a lot !!
> Thomas Merkling
> 
> 
> Le 20:59, Ben Bolker a écrit :
> On 01/20/2011 11:40 AM, espesser wrote:
>>>>
>>>>   Here is a small function to compute the dispersion of
> a  binomial  model, according to  a previous answer of D. Bates on the
> topic:
> 
>   dispersion_glmer<- function(modelglmer)
> {
> 
> ## computing  estimated scale  ( binomial model)
> #following  D. Bates :
> #That quantity is the square root of the penalized residual sum of
> #squares divided by n, the number of observations, evaluated as:
> 
> n<- length(modelglmer at resid)
> 
> return(  sqrt( sum(c(modelglmer at resid, modelglmer at u) ^2) / n ) )
> }
> 
> 
> 
> -- Robert Espesser
> CNRS UMR 6057 - Université de Provence
> 5 Avenue Pasteur - BP 80975
> 13604 AIX-EN-PROVENCE Cedex 1
> 
> Tel: +33 (0)442 95 36 26
> 
>>>> Le 20/01/2011 16:59, Thomas Merkling a écrit :
>>>>> Dear list members,
>>>>>
>>>>> I am trying to fit a binomial GLMM and I wonder if there is
>>>>> overdispersion. I'm not sure to know how to do it. I tried to fit with
>>>>> "quasibinomial" family but apparently it doesn't exist anymore in lme4.
>>>>>
>>>>> I also tried this but I am not sure that it is true for mixed models.
>>>>>
>>>>> model<-lmer(propNb~SexA*SexB*AgeA+(1|Nest),data=baba,family="binomial")
>>>>>
>>>>> k<- attr(logLik(model),"df") #
>>>>> n<- length(fitted(model))
>>>>> pearsonresid<- (1/(n-k)) * sum(resid(model,"pearson")2) # 1.731892
>>>>> dev<- deviance(model)/(n-k) #2.378512
>>>>>
>>>>> One more thing: how to deal with this model if there is
>>>>> overdispersion ?
>>>>>
>>>>> Thanks by advance,
>>>>> Best,
> 
>    If there is overdispersion, the current advice is to fit an
> observation-level random effect:
> 
> baba$obs<- 1:nrow(baba)
> 
> model_OD<-
> glmer(propNb~SexA*SexB*AgeA+(1|Nest)+(1|obs),data=baba,family="binomial")
> 
> 
>>
>>

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