[R-sig-ME] Bayesian Conway-Maxwell-Poisson distribution

[Célia Sofia Moreira]

Dear all,

I'm performing some mixed-modeling analyses using the
Conway-maxwell-Poisson distribution, from the glmmTMB package (my response
variables are underdispersed). I would like to complement some results from
this frequentist statistics with Bayesian results, mainly because the
significance of some (glmmTMB) results are borderline, i.e., are marginally
significant. More specifically, I would like to compute the (Bayesian)
evidence ratio in order to compare two quantities.

In the Bayesian context, I usually use the brms package. Unfortunately,
this package has no specific family to deal with underdispersed count data
(it has only for overdispersed count data). As far as I know, there are no
Bayesian packages with specific families for underdispersed count data.

So, I see two main options, and I would be grateful if you could tell me
your opinion about the best way to follow:

1) performing post-hoc MCMC with glmmTMB, as described in
https://cran.r-project.org/web/packages/glmmTMB/vignettes/mcmc.html
and then use the output model to obtain the evidence ratios (through brms,
for example). However, In this case, I don't know if it is possible to
define the priors and, in the affirmative case, how to do it. Do you?

2) using the gamma-count distribution (R code available at
https://discourse.mc-stan.org/t/brms-and-conway-maxwell-poisson-distribution/7368/6
). However, in this case, I have to work with an unfamiliar package (to me;
some difficulties may arise further)...

Can you please tell me your opinion about this problem?

Kind regards,
csm

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