[R-sig-ME] Observation-level random effect to model overdispersion
Jarrod Hadfield
j.hadfield at ed.ac.uk
Mon Mar 21 13:17:17 CET 2011
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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>
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