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

[Ben Bolker]

On 03/21/2011 09:36 AM, Ryan King wrote:
> Yes, you are correct.  If a lognormal distribution bothers you, you 
> can definitely combine conjugate RE for over-dispersion and
> log-normal RE elsewhere in the predictor.  In the poisson example,
> you could imagine doing random-effect negative-binomial regression. 
> http://arxiv.org/abs/1101.0990 implemented that using SAS NLMIXED.

 If you want to stay within the R world, and if you have only a single
random effect, I would recommend glmmADMB.  If you have multiple random
effects, we are working on a multiple-random-effect version of glmmADMB ...


> 
> Heuristically, you end up with non-zero residuals because the 
> assumption of normality for the subject-level effect adds an L2 
> penalty away from the maximum-likelihood estimate, which would be
> the entire residual.
> 
> Ryan King Dept Health Studies University of Chicago
> 
> On Mon, Mar 21, 2011 at 8:09 AM, 
> <r-sig-mixed-models-request at r-project.org> wrote:
>> Message: 1 Date: Mon, 21 Mar 2011 12:51:39 +0100 From: "M.S.Muller"
>> <m.s.muller at rug.nl> To: r-sig-mixed-models at r-project.org Subject:
>> [R-sig-ME] Observation-level random effect to model overdispersion 
>> Message-ID: <7520f6c92de64.4d8749db at rug.nl> Content-Type:
>> text/plain; charset=us-ascii
>> 
>> 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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