[R] How to tell if there is overdispersion in a GLMM?

[Ben Bolker]

maggy yan <kiotoqq <at> gmail.com> writes:

> 
> I read something on http://glmm.wikidot.com/faq, under "How can I deal with
> overdispersion in GLMMs?":
> 
> library(lme4)  ## 1.0-4set.seed(101)
> d <- data.frame(y=rpois(1000,lambda=3),x=runif(1000),
>             f=factor(sample(1:10,size=1000,replace=TRUE)))
> m1 <- glmer(y~x+(1|f),data=d,family=poisson)
> overdisp_fun(m1)
  ##        chisq        ratio          rdf            p
> ## 1026.7780815    1.0298677  997.0000000    0.2497659
> library(glmmADMB)  ## 0.7.7
> m2 <- glmmadmb(y~x+(1|f),data=d,family="poisson")
> overdisp_fun(m2)   
  ##        chisq        ratio          rdf            p
> ## 1026.7585031    1.0298480  997.0000000    0.2499024
> 
> In both case, the chisq is > rdf, does it mean there is over dispersion?
> 
> thanks for any help
> 

 Off-topic here, but:

  the residual deviance is greater than the residual degrees
of freedom, but only a little bit (3%).  So, technically, there
is overdispersion here, but not more than expected if the underlying
data generating process was not overdispersed
 (p-value = 0.25).  Which is a good thing
because the data are generated from a Poisson distribution, so
the null hypothesis is actually true.