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

[Murray Jorgensen]

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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-- 
Dr Murray Jorgensen      http://www.stats.waikato.ac.nz/Staff/maj.html
Department of Statistics, University of Waikato, Hamilton, New Zealand
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