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

[Douglas Bates]

On Sat, Dec 13, 2008 at 12:46 PM, Murray Jorgensen
<maj at stats.waikato.ac.nz> 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.

In another thread I posted a long-winded manifesto regarding the types
of models that will be fit by lme4-1.0

John, you may be uneasy but I need to get a completed version of this
code out some time (it is way overdue), so I am truncating the list of
possible models at the ones I describe there.

I appreciate all the contributions to this discussion.
>
> 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
> Email: maj at waikato.ac.nz    majorgensen at ihug.co.nz      Fax 7 838 4155
> Phone  +64 7 838 4773 wk    Home +64 7 825 0441    Mobile 021 139 5862
>
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