[R-sig-ME] glmmadmb Negative binomial dispersion parameter

Highland Statistics Ltd highstat at highstat.com
Tue Feb 23 19:43:12 CET 2016

> Message: 1
> Date: Tue, 23 Feb 2016 15:02:48 +0100
> From: Marte Lilleeng <mlilleeng at gmail.com>
> To: r-sig-mixed-models at r-project.org
> Subject: [R-sig-ME] glmmadmb Negative binomial dispersion parameter
> Message-ID:
> 	<CAM-hW5cun5sXzyf-WrCLF2CGJjfQeD1nTnnccAZ213kbSqDSvA at mail.gmail.com>
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> Hello everyone.
> I wonder if you can help me with the following questions?
> 1) How is the Negative binomial dispersion parameter calculated in glmmadmb?
That is a very good question. While writing this email I have a series 
of help files open which explain how mgcv is estimating the theta, and 
how glm.nb from MASS is doing it. Performance iteration, outer 
iteration, estimating the theta so that the dispersion statistic is 1, 
or via AIC. So..the answer to your question depends very much which 
strategy the programmers of glmmADMB have followed. Have a look at the 
http://admb-project.org/ website. Maybe you can find your answer there.

GLMs in which the variance term contains an extra parameter (Gaussian, 
Gamma, beta-binomial) cannot be overdispersed. The Poisson and the 
binomial GLM don't have this facility, so they can be overdispersed. 
Strictly speaking the NB GLM is not a GLM (it is not part of the 
exponential family).

The algorithm for NB GLM ping-pongs between a glm algorithm and an 
algorithm for getting the theta (at least this is what glm.nb is doing).
So..strictly speaking when the algorithm is doing its glm leg, it can be 
overdispersed (dispersion statistic > 1).

> 2) Is there,as for mixed effects poisson models (glmer), a *rule of thumb*
> for when the dispersion parameter is representing trouble (overdispersion)?
> I learned from Zuur and Ileno that for a mixed effects poisson mod the
> dispersion is ok as long as it is not above 1.3-1.4(calculated this way;
> E <- residuals (modelname)
> pb <- length(fixef(modelname)+1) # +1 due to random intercept variance
> overdisp <- sum(E^2)/(nrow(dataset)-pb)

You have to add another '+1' due to the theta from the NB GLM.

It is perhaps better to simulate 10,000 times the response variable from 
the fitted model and see how the dispersion statistic varies. Make a 
histogram of the 10,000 dispersion statistics and add a big dot for the 
one you found for your original data set.

You can do the same for the number of zeros, maximum value, etc.

> 3) How do you recommend to do the model validation for glmmadmb with
> negative binomial error structure?
As usual. Plot residuals vs everything you have. It is also interesting 
to apply table() on each of the 10,000 simulated data sets, or calculate 
an average table(). And plot that vs the table() for the original data.

Kind regards,


> Best regards from
> "New to mixed models with NB", Marte Lilleeng
> 	[[alternative HTML version deleted]]

Dr. Alain F. Zuur

First author of:
1. Beginner's Guide to GAMM with R (2014).
2. Beginner's Guide to GLM and GLMM with R (2013).
3. Beginner's Guide to GAM with R (2012).
4. Zero Inflated Models and GLMM with R (2012).
5. A Beginner's Guide to R (2009).
6. Mixed effects models and extensions in ecology with R (2009).
7. Analysing Ecological Data (2007).

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