[R-sig-ME] question on nbinom1

[Mollie Brooks]

I don’t have a copy of Hardin & Hilbe 2007 on hand, but I answered a few of your questions below.

> On 10Oct 2020, at 3:34, Don Cohen <don-lme4 using isis.cs3-inc.com> wrote:
> 
> 
> In response to a question about use of nbinom1 in glmTMB, specifically
> about this paper by VerHoef J.M. & Boveng:
> https://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1141&context=usdeptcommercepub
> which says that AIC cannot be used to choose between a quasi-Poisson model
> and a negative binomial,
> 
> Ben Bolker writes:
> 
>>    nbinom1 is *not* quasi-: see Hardin & Hilbe 2007 as suggested in 
>> ?nbinom1.  (It can't be fitted in a standard GLM framework, since this 
>> parameterization of the nbinom doesn't fit into the exponential family, 
>> but glmmTMB is more flexible than that ...)
> 
> I've been trying to figure out what Hardin & Hilbe have to say about this,
> and so far failing to find the connection.
> (BTW, is nbinom1 the same as what they call NB-C ?)
> 
> Does "nbinom1 is *not* quasi-" mean that the AIC reported when I use 
> nbinom1 really IS comparable to the one reported when I use nbinom2?

Yes

> And that loglik is actually being computed for a "real" distribution?

Yes 

> Does it matter whether I also use random effects, zero inflation, 
> offset, etc. ?

No it doesn’t matter; the AIC is comparable when fitting those types of models. 

Some examples are 
https://cran.r-project.org/web/packages/glmmTMB/vignettes/glmmTMB.pdf <https://cran.r-project.org/web/packages/glmmTMB/vignettes/glmmTMB.pdf>
and 
appendix A here https://journal.r-project.org/archive/2017/RJ-2017-066/RJ-2017-066.pdf <https://journal.r-project.org/archive/2017/RJ-2017-066/RJ-2017-066.pdf>

cheers,
Mollie

> 
> Alternatively, if AIC for nbinom1 is really NOT comparable to AIC for the
> other (real?) distributions, how is one supposed to determine which model
> better fits the data?  VerHoef suggests trying to determine whether the
> variance for different subpopulations with different means more closely
> resembles linear or quadratic functions of the mean, but this is not at
> all clear in the data I'm trying to analyze.
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