[R-sig-ME] 3-level binomial model

[David Duffy]

On Thu, 17 Apr 2008, Doran, Harold wrote:

> I haven't really followed this thread, but I'd disagree and say that the
> variance components have a very meaningful interpretation. If the fixed
> effects are the log-odds of success, then the variance component would
> be the variability in the log-odds for whatever units are of interest.
>
> On the issue of the ICC for the GLMM, to me this is all hocus-pocus.
> This is a meaningful statistic in the world of linear models because the
> within-person variance (or your level 1 variance) is assumed
> homoskedastic. But, this is not true with generalized linear models.
>
> Now, you can compute it as you did by fixing the level 1 variance at the
> logistic scale and you can give reviewers whatever they want, but this
> doesn't make it meaningful. So, waving a magic wand to make GLMM
> estimates look like linear estimates is neat, but I think the better
> path is to show your reviewers why this isn't a meaningful statistic.
>

Well, in the area of genetics, people have been quite happily doing just 
this since 1918, under the "Multifactorial Threshold Model", which is the 
equivalent probit model.  And if you look at Yazdi et al J Dairy Sci 
85:1563-1577 (2002), you will see an approach to derive a similar 
meaningful number under a Weibull mixed model (ICC <-> heritability). 
There, the interest is in giving a number that represents the response to 
selection of different traits that all contribute to financial return.

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   \_,-._/
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