[R-sig-ME] Additive versus multiplicative overdispersion modeling

[Ned Dochtermann]

First posting to the list, prior to sending this out I've tried
searching the mixed model list, other lists and anything google could
pick up.

I am currently trying to calculate repeatability estimates
(intra-class correlation coefficients) following Nakagawa & Schielzeth
(2010, Biol.Rev. Repeatability for Gaussian and non-Gaussian data: a
practical guide for biologists. online early). The details of my
models shouldn't be important except that I originally fit the models
using binomial error structures and a logit link. Nakagawa and
Schielzeth (henceforth N&S) specify that repeatability estimates
differ based on whether additive or multiplicative overdispersion
modelling is conducted.

N&S define multiplicative as when the dispersion parameter is
estimated but that residual variance is fixed to one. Additive is
defined as having the residual variance estimated and the dispersion
parameter fixed to one. These definitions are based on Browne et al.
(2005, J. Roy. Stat. Soc A, 168:599-613).

Based on my reading of the family objects description it seems that
using the quasibinomial family would correspond to the multiplicative
overdispersion modelling and the binomial family would correspond to
additive overdispersion modelling.

Is this conclusion about multiplicative vs. additive correct or am I
missing something? I do realize that when the dispersion parameter is
estimated as being close to one under a quasibinomial model then the
results should be close to what you'd get with a binomial approach
which makes me think I am missing something (since the multiplicative
model would have the residual variance fixed).

Thank you for any help you can provide.
Ned Dochtermann



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Ned Dochtermann
Department of Biology
University of Nevada, Reno
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