# [R-sig-ME] different overdispersion parameter for binomial GLMM in, lme4, glmmADMB and glmmTMB (Muldoon, Ariel)

Highland Statistics Ltd highstat at highstat.com
Fri Mar 16 22:04:14 CET 2018

```> Ben, sorry but I am bit confused by your answer. If I understand
> correctly, the approach you would recommend is to calculate the
> dispersion parameter on the binomial model and if there is
> overdispersion compare models with different ways to deal with it (e.g
> observation-level random effects and beta-binomial) to the binomial one
> to find out which ones fits the data better. Is that correct? And so
> there would be no point in calculating the dispersion parameter for the
> OLRE and beta-binomial model and see how much it goes down?
>
> Cheers,

Correct. Overdispersion/underdispersion is only relevant for
distributions in which the variance is determined by the mean. Like the
Poisson: mean(Y) = var(Y)  and the binomial: E(Y) = N * pi and var(Y) =
Pi * N * (1 - Pi).

No need to check for overdispersion for the normal, Gamma, inverse
Gaussian, beta-binomial, and beta distributions. These distributions
have an extra parameter (like the variance in the normal distribution)
in the variance term. Having said that...I am still confused why the
Negative binomial GLM can be overdispersed. I guess that is because the
NB GLM is not a real GLM and iterates between two algorithms (when doing
frequentist analysis). I guess (again) it is more about whether the
functional form of the NB variance is correct...or not.

Instead of using a dispersion statistic based on Pearson residuals
(coming from models with fancy random effects) it is perhaps better to
simulate data from your model and compare the variation in the simulated
data with the variation in the observed data. Or do what Ben Bolker
suggested a few days/weeks ago...simulate data and compare the
corresponding residuals with the original residuals.

Alain

--

Dr. Alain F. Zuur
Highland Statistics Ltd.
9 St Clair Wynd
AB41 6DZ Newburgh, UK
Email: highstat at highstat.com
URL:   www.highstat.com

And:
NIOZ Royal Netherlands Institute for Sea Research,
Department of Coastal Systems, and Utrecht University,
P.O. Box 59, 1790 AB Den Burg,
Texel, The Netherlands

Author of:
1. Beginner's Guide to Spatial, Temporal and Spatial-Temporal Ecological Data Analysis with R-INLA. (2017).
2. Beginner's Guide to Zero-Inflated Models with R (2016).
3. Beginner's Guide to Data Exploration and Visualisation with R (2015).
4. Beginner's Guide to GAMM with R (2014).
5. Beginner's Guide to GLM and GLMM with R (2013).
6. Beginner's Guide to GAM with R (2012).
7. Zero Inflated Models and GLMM with R (2012).
8. A Beginner's Guide to R (2009).
9. Mixed effects models and extensions in ecology with R (2009).
10. Analysing Ecological Data (2007).

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