[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
redundant.
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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>
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