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

[Ned Dochtermann]

Thanks a lot, if that is indeed the case it makes calculating
repeatabilities per N&S quite straightforward for the multiplicative
models (quasibinomial & quasipoisson) since the relevant term to
include in the denominator would just be (summary(model)@sigma)^2
(multiplied by (pi^2)/3 ). Of course I still can't figure out how to
get the needed information from the additive models, i.e. the residual
of the distribution specific variance.


Ned

On Thu, Aug 19, 2010 at 10:00 PM, David Duffy <davidD at qimr.edu.au> wrote:
> 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
>