[R-sig-ME] Observation-level random effect to model overdispersion

[Jarrod Hadfield]

Hi,

Your intuition is correct: using an observation-level random effect is  
the same as using a log-normal mixing distribution if the log-link is  
used: the marginal distribution of the observation-level effects are  
assumed to be normal. It goes back to HINDE J (1982) GLIM 82-109  at  
least.

Jarrod

On 21 Mar 2011, at 11:51, M.S.Muller wrote:

> Dear all,
>
> I'm trying to analyze some strongly overdispersed Poisson- 
> distributed data using R's mixed effects model function "lmer".  
> Recently, several people have suggested incorporating an observation- 
> level random effect, which would model the excess variation and  
> solve the problem of underestimated standard errors that arises with  
> overdispersed data. It seems to be working, but I feel uneasy using  
> this method because I don't actually understand conceptually what it  
> is doing. Does it package up the extra, non-Poisson variation into a  
> miniature variance component for each data point? But then I don't  
> understand how one ends up with non-zero residuals and why one can't  
> just do this for any analyses (even with normally-distributed data)  
> in which one would like to reduce noise.
>
> I may be way off base here, but does this approach model some kind  
> of mixture distribution that's a combination of Poisson and whatever  
> distribution the extra variation is? I've read that people often use  
> a negative binomial distribution (aka Poisson-gamma) to model  
> overdispersed count data in which they assume that the process is  
> Poisson (so they use a log link) but the extra variation is a gamma  
> distribution (in which variance is proportional to square of the  
> mean). The frequently referred to paper by Elston et al (2001)  
> describes modeling a Poisson-lognormal distribution in which  
> overdispersion arises from errors taking on a lognormal  
> distribution. Is the approach of using the observation-level random  
> effect doing something similar, and simply assuming some kind of  
> Poisson-normal mixed distribution? Does this approach therefore  
> assume that the observation-level variance is normally distributed?
>
> If anyone could give me any guidance on this, I would appreciate it  
> very much.
>
> Martina Muller
>
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