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

[Paul Johnson]

Hi Marte,

In answer to point 2 (adapted from a comment i made on the R-space FB group)...

My general approach is not to bother testing for overdispersion in GLMMs, but to assume it's there and model it as a matter of course, using either the OLRE approach with glmer (see Xavier Harrison's paper https://peerj.com/articles/616/) or negative binomial with glmmADMB (I've never used glmer.nb - the help file used to give a health warning, but I see that's gone). Modelling overdispersion is simply modelling unexplained variation at the observation level, so to fit a Poisson or binomial GLMM that doesn't allow for overdispersion is effectively assuming that the model explains all the variation, which is almost never a reasonable assumption (at least in biology). I don't agree with the approach of ignoring it if either it isn't significant or if the OD index you showed is low (< 1.3-1.4). This still seems to me a Ignoring a potentially substantial amount of variance and ignoring it could still have negative consequences such as an inflated false positive rate for tests and over-optimistic (narrow) CIs.

Including a term for overdispersion (when possible) in a GLMM is pretty much the same as including a residual error term in a simple OLS linear regression model, except that in the linear regression model there is no other source of random variation so we'd never consider leaving it out.

A caveat is that overdispersion can be caused by a mis-specified model so it's important to try to identify this before assuming that all the overdispersion is due to unexplained variation.

All the best,
Paul

On Tue, Feb 23, 2016 at 2:07 p.m., Marte Lilleeng <mlilleeng at gmail.com<mailto:mlilleeng at gmail.com>> wrote:

Hello everyone.
I wonder if you can help me with the following questions?

1) How is the Negative binomial dispersion parameter calculated in glmmadmb?

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)

3) How do you recommend to do the model validation for glmmadmb with
negative binomial error structure?

Best regards from
"New to mixed models with NB", Marte Lilleeng

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