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

[Ben Bolker]

   One reference that uses ordinal regression in a similar situation
(litter size of Florida panthers) is
http://link.springer.com/article/10.1007/s00442-011-2083-0 ("Does
genetic introgression improve female reproductive performance? A test on
the endangered Florida panther")

  Not sure about the number-of-random-effects error: a reproducible
example would probably be needed (smaller is better!)

  Ben Bolker


On 16-12-06 08:41 AM, Simone Santoro 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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> 
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