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- Poisson in glimmix with underdispersion

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01-16-2015 08:50 AM

Dear all,

I am performing a glimmix model on count data (brood size: number of nestlings in a nest). The distribution ranges from 1 to 6 nestlings per nest. I am trying to test a fixed factor (treatment) with two levels. The models also includes a random term (the brood identity where the parents were born). The model shows underdispersion as the generic chi-square /DF shows a 0.29 value, and the distribution shows a large peak at the central value of 3 chicks. First, I am unsure about the necessity of correcting for underdispersion here. Apparently, there is a debate on this as by correcting it the possibility of inflating type II errors increases. I would want to ask you about your opinion on this question. Second, I do not know how to fix it, how to correct underdispersion. Please, see the model below. What syntaxis should be added? Finally, I would also know if some correction for the degrees of freedom must be done. I have tried Satt but it shows some problems as the DF changes to 1 (some problem with the random term, which is never significant).

proc glimmix ;

class idbrood treatment ;

model broodsize= treatment/dist=poisson link=log ;

random idbrood/group=treatment;

covtest/wald;

run;

I would be very grateful for your help and comments.

Thanks in advance,

Carlos

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01-16-2015 11:16 AM

I think the underdispersion problem is something to note in the discussion, but should not be a stopper in the analysis.

The only underdispersion technique I can think of is to consider a mixture of two overlapping distributions that "pile up" at 3 nestlings per nest. Unfortunately, unless you were spectacularly lucky and Idbrood is a strong predictor of the source of the distribution, the procedure in SAS (PROC FMM) doesn't accommodate random effects..

Steve Denham

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01-16-2015 04:34 PM

Dear Steve,

thanks for your quick answer. An R user has suggested me that R can do the correction for underdispersion in mixed Poisson models by specifying the scale parameter, I supppose that it is similar to that used in SAS genmod (dscale or similar), however, when used on my data it strongly reduced the alpha value, so it seems to be quite tricky.

Really, the proc fmm does not work well on my dataset due to random effects.

thanks anyway,

Carlos

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01-16-2015 04:56 PM

You can do the same thing with a

random _residual_;

term in your model. But I recommend against it. By doing so, you are entering the realm of quasi-likelihood, where the "distribution" is no longer what you think it is (there is no discrete distribution that has the form you get with "Poisson" and over- or under-dispersion). When possible, deal with a real distribution. Your underdispersion is trivial.

By the way, if you really want to assess goodness of fit, you should be using method=laplace rather than the default pseudo-likelihood method. That way, you will get a likelihood on the scale of the data not on the scale of pseudo-data.

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01-16-2015 04:58 PM

I also question your need for different variances for each treatment. Did you look at this to see if it is justified? You can compare models with and without the group effect for the random term by comparing log likelihoods, but only if you use method=laplace.