[R-sig-ME] GLMM for underdispersed count data: Conway-Maxwell-Poisson and Ordinal

[Simone Santoro]

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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