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

[Ryan Simmons]

Hi csm,

There is a package called "combayes" (https://github.com/cchanialidis/combayes) for Bayesian inference of Conway-Maxwell-Poisson regression models. I don't know much about this package, but it appears to at least be well-documented, and if nothing else then looking at the source code may guide you in developing a solution. The paper describing the algorithms used in this package is called "Efficient inference for COM-Poisson regression models" published in Statistics and Computing, May 2018, Volume 8, Issue 3, p.595-608 by Charalampos Chanialdis, Ludger Evers, Tereza Neocleous, and Agostino Nobile. The doi is: https://doi.org/10.1007/s11222-017-9750-x, and you can find it online here: https://link.springer.com/article/10.1007/s11222-017-9750-x. 

Good luck!

-Ryan

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Date: Wed, 23 Jan 2019 12:19:48 +0000
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Subject: [R-sig-ME] Bayesian Conway-Maxwell-Poisson distribution
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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://urldefense.proofpoint.com/v2/url?u=https-3A__cran.r-2Dproject.org_web_packages_glmmTMB_vignettes_mcmc.html&d=DwICAg&c=imBPVzF25OnBgGmVOlcsiEgHoG1i6YHLR0Sj_gZ4adc&r=szMipnZzQMIctqnszKsX-AUNBHtRn663-NaJh5_rHBE&m=OSZv1-WYaULDAcsvdVobBHQNa1WmbZwz0TLojWBC5Y8&s=EE3SUxLx3KVRUdyPXQWLbr30Az-XaNQkp9hZzPOxYZQ&e=
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://urldefense.proofpoint.com/v2/url?u=https-3A__discourse.mc-2Dstan.org_t_brms-2Dand-2Dconway-2Dmaxwell-2Dpoisson-2Ddistribution_7368_6&d=DwICAg&c=imBPVzF25OnBgGmVOlcsiEgHoG1i6YHLR0Sj_gZ4adc&r=szMipnZzQMIctqnszKsX-AUNBHtRn663-NaJh5_rHBE&m=OSZv1-WYaULDAcsvdVobBHQNa1WmbZwz0TLojWBC5Y8&s=45Hcvw8fez6Qc8Ptv5ag2eHHdu5B0qKnInnoZz4Yn2o&e=
). 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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