GLMM for underdispersed count data: Conway-Maxwell-Poisson and Ordinal

The Conway-Maxwell-Poisson may well be the way to go here; I?ll note only that I have sometimes found underdispersed counting data being driven by excess zeroes. If zero-inflation of some kind is in fact the culprit, and you still wish to use multi-level modeling, the brms front-end for Stan offers a variety of easy-to-use fitting options for zero-inflation / hurdle / adjustment.



Best,

Jonathan



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From: Mollie Brooks<mailto:mollieebrooks at gmail.com>
Sent: Wednesday, December 7, 2016 7:36 PM
To: Simone Santoro<mailto:santoro at ebd.csic.es>
Cc: r-sig-mixed-models at r-project.org<mailto:r-sig-mixed-models at r-project.org>
Subject: Re: [R-sig-ME] GLMM for underdispersed count data: Conway-Maxwell-Poisson and Ordinal



Dear Simone,

I?ve been working on adding the Conway-Maxwell-Poisson distribution to the glmmTMB package. It isn?t published yet, but I?ve tested it with simulated data and 2 real data sets. It seems to be working well, so I plan to introduce it in a manuscript on Biorxiv in the near future. You?re welcome to try it with your data and tell me how it goes.

First, you?ll have to install the genpois branch of glmmTMB with the following

devtools::install_github("glmmTMB/glmmTMB/glmmTMB", ref="genpois")

Then, you could fit your model with this code

FMCMP <- glmmTMB(fledges ~ habitatF * (areaPatchFath + poligF01 +
StdLayingDate + ageFath1 + ageMoth1) + (1|year) + (1|ringMoth) +
(1|ringFath), data = datiDRS, family="compois")

For an explanation of the dispersion parameter, see ?sigma.glmmTMB

If you want to try it out on simulated data, there?s an rCMP function available here
https://github.com/James-Thorson/Conway-Maxwell-Poisson <https://github.com/James-Thorson/Conway-Maxwell-Poisson>

cheers,
Mollie

???????????
Mollie E. Brooks, Ph.D.
Postdoctoral Researcher
National Institute of Aquatic Resources
Technical University of Denmark

On 6Dec 2016, at 14:41, Simone Santoro <santoro at ebd.csic.es> wrote:

Dear all,

I am trying to find an appropriate GLMM (with temporal and individual
crossed random effects) to model underdispersed count data (clutch
size). I have found several possible ways of doing that. A good
distribution for data like this would seem to be the
Conway-Maxwell-Poisson but I have not found a way of using it within a
GLMM in R (I have asked here
<http://stats.stackexchange.com/questions/249738/how-to-define-the-nu-parameter-of-conway-maxwell-poisson-in-spamm-package>
and here
<http://stats.stackexchange.com/questions/249798/conway-maxwell-poisson-with-crossed-random-effects-in-r>).
I have seen that Ben Bolker suggested (here
<https://stat.ethz.ch/pipermail/r-sig-mixed-models/2014q1/021945.html>and
here
<http://stats.stackexchange.com/questions/92156/how-to-handle-underdispersion-in-glmm-binomial-outcome-variable>)
to use an ordinal model in cases like this(e.g. _ordinal:clmm_). I have
tried this solution and the results I obtain makes (biological) sense to
me. However, I wonder why but I cannot put all the three crossed random
effects I have in the clmm model (_Error: no. random effects (=1254) >=
no. observations (=854)_) whereas it is not a problem for the glmer
model (the no. of levels of each single random effect does not exceed 854)*.
Beyond that, and that's what I would like to ask you, *I cannot find a
reference to justify I used the ordinal model* to deal with
underdispersed count data (referee will ask it for sure).
Best,

Simone

* FMglmer<- glmer(fledges ~ habitatF * (areaPatchFath + poligF01 +
StdLayingDate + ageFath1 + ageMoth1) + (1|year) + (1|ringMoth) +
(1|ringFath), data = datiDRS)
   FMclmm<- glmer(as.factor(fledges)~ habitatF * (areaPatchFath +
poligF01 + StdLayingDate + ageFath1 + ageMoth1) + (1|year) +
(1|ringMoth) + (1|ringFath), data = datiDRS)


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