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

[Jarrod Hadfield]

Hi Ned,

You can get the additive residual term of N&S by fitting an  
observation-level random effect (i.e. one effect for each datum). You  
will need the latest version of lme4 for this (not available for Mac).  
If the data are binary you can't estimate the residual, so it is usual  
just to set it to zero.

Cheers,

Jarrod


Quoting Ned Dochtermann <ned.dochtermann at gmail.com>:

> 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
>>
>
> _______________________________________________
> R-sig-mixed-models at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>
>



-- 
The University of Edinburgh is a charitable body, registered in
Scotland, with registration number SC005336.