question on nbinom1
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 at 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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