[R-sig-ME] single argument anova for GLMMs (really, glmer, or dispersion?)

Robert Kushler kushler at oakland.edu
Sun Dec 14 04:59:36 CET 2008

Doesn't it make sense to think of the "gamma mixture of Poissons" as
a Poisson GLM with a gamma-distributed random (intercept) effect?  In other
words, it's a GLMM with a gamma distribution instead of gaussian.  Adding
another (gaussian) random effect to a negative binomial model seems a bit

Regards,   Rob Kushler

Murray Jorgensen wrote:
> I thought I might note that zero-inflated count data and negative 
> binomial data can both be seen as cases where the response variable 
> follows a mixture distribution. In the ZIP case a mixture of a constant 
> [ Poisson(0) or Poisson(tiny) with another Poisson], in the negative 
> binomial case a gamma mixture of Poissons [which might be approximated 
> by a finite mixture].
> John is "uneasy with glmer's restriction to models where the error 
> family variance can only be modified by addition on the scale of the 
> linear predictor." Mixtures would be one mechanism for introducing other 
> variance patterns into the model.
> Murray Jorgensen
> Ben Bolker wrote:
>>> I think that this is fair enough and well put, John, but I'm going to
>>> push back in the other direction with a hypothetical example.  Let's
>>> say that you have your over-dispersed count data.  What do you lose if
>>> you simply take some convenient and credible transformation of the
>>> response variable and then use lme, paying close attention to your
>>> conditional distribution plots? 
>>   Besides the aesthetic preference for fully specified models etc.
>> (although there's also the danger of forgetting that "all models
>> are wrong etc." and believing the model too much), the most common
>> reason in ecological contexts for not being able to get away with
>> transformation is that the data are zero-rich (someone mentioned
>> zero-inflated/hurdle models earlier in this discussion, which
>> basically amounts to modeling presence/absence [either of
>> "structural" zeros or of all zero values] and conditional
>> density separately).  There's nothing you can do to transform
>> a spike in the data (at zero or elsewhere) into anything
>> other than a spike ...
>>   Ben Bolker
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