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

[David Duffy]

On Thu, 19 Aug 2010, Ned Dochtermann wrote:

> 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.
[SNIP]
> 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.

Yes.  Browne et al say they are using the "additive" approach because it 
has a proper likelihood.

If you are interested in repeatability of binary measures, there are lots 
of perfectly good "direct" measures.  The thing about the GLMM variance 
components is that they are up in the latent variable part of the model. 
If you are using a probit-normal, you are getting (essentially) 
tetrachoric correlations, that is, estimating the correlation between the 
"true" continuous measures that are being arbitrarily dichotomized to give 
you your binary outcome.  For biometrical geneticists, this is a regarded 
as a good thing (Yule might disagree ;)), but might not be as useful for, 
say, assessing different clinical tests.  It really does depend on your
actual problem.

Cheers, David Duffy.
-- 
| David Duffy (MBBS PhD)                                         ,-_|\
| email: davidD at qimr.edu.au  ph: INT+61+7+3362-0217 fax: -0101  /     *
| Epidemiology Unit, Queensland Institute of Medical Research   \_,-._/
| 300 Herston Rd, Brisbane, Queensland 4029, Australia  GPG 4D0B994A v