Question on parametrization and underdispersion in genpois family of glmmTMB

Hi,

From what I know but not sure, here are a few responses.

1. Parametrization in glmmTMB
glmmTMB uses the Joe & Zhu (2005) parametrization of the Generalized
Poisson distribution, not the original Consul & Famoye (1992)
parametrization directly.
This was ported via the HMMpa package, and the documentation reflects that.
Joe & Zhu (2005) is a reparametrization of the Consul?Famoye GP that is
more stable numerically for GLM fitting.

2. Underdispersion in glmmTMB
Yes, negative values of the dispersion parameter (alpha) are allowed in
glmmTMB.
This means underdispersion is supported. More precisely  glmmTMB::genpois
covers both overdispersion (alpha>0) and underdispersion (alpha<0).

Others could confirm ?

Best,

Le 8 sept. 2025 ? 10:40, HATICE T KUBRA AKDUR <hkubrasenol at gmail.com> a

?crit :

?Dear glmmTMB Developers,

I am currently working on a methodological paper regarding  mixed-effects
count models, where the Generalized Poisson distribution plays an

important

role. I have been using the glmmTMB package and I have a couple of
questions regarding the implementation of the genpois family:

  1.

  *Parametrization*:
  -

     According to the package documentation, the genpois family is based
     on Consul & Famoye (1992), but the implementation was taken from the
     HMMpa package, which in turn follows Joe & Zhu (2005).
     -

     Could you please clarify the exact parametrization used in glmmTMB
     for the Generalized Poisson? F
     2.

  *Underdispersion*:
  -

     In the original Consul?Famoye formulation, negative values of the
     dispersion parameter allow modeling underdispersed data.
     -

     Does the glmmTMB implementation of genpois allow negative dispersion
     parameters, and thus support underdispersion? Or is the parameter
     constrained to nonnegative values (overdispersion only)?

This clarification would be very valuable for correctly citing the

package

and explaining the underlying assumptions in my work.

Thank you very much in advance for your time and for maintaining such an
excellent and widely used package.

Best regards,
--
Assoc. Prof. Dr. Hatice T. Kubra AKDUR
Department of Statistics, Faculty of Science, Gazi University
06500 Teknikokullar ANKARA, TURKEY
Phone: +90 553 324 5380
Email: hatice_senol at wsu.edu
https://scholar.google.com/citations?user=_DLBsl4AAAAJ&hl=en

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