[R-sig-ME] residual variances in glmer

David Duffy David.Duffy at qimr.edu.au
Mon Dec 8 23:07:26 CET 2008

On Mon, 8 Dec 2008, Hervé CHAPUIS wrote:

> Hello every one.
> I am a real R-mix models-newbie. A colleague told me I should ask  the  list.
> Well, when dealing with  discrete traits  in animal genetics, we have many 
> possibilities :
> - use an home-made program based, for instance, on Gianola & Foulley (1993) 
> algorithm.
> - treat the data as a classical gaussian performance, use a linear mixed 
> model (lmer works fine) and then compute the heritability coefficient on the 
> observed scale  as h2 = 4 x sire_variance (sire_variance + dam_variance 
> + residual_variance).
> After that, use the Dempster & Lerner formula to obtain the heritability on 
> the  underlying scale.
> - or use directly a general linear mixed model.
> That's what I have done but I have been puzzled by the results.
> On simulated data, (I have simulated a vector of gaussian performances 
> accounting for Mendelian rules, before transforming them into binary data 
> through a given threshold value)  the first two options give me  "good" 
> results and an estimated h² reasonably close  to the expected value.
> If  I use glmer instead of lmer, I still obtain a result but I cannot safely 
> obtain the h2 assuming that the residual variance is 1, can I ?
> If so, the estimated h2 is very high, if not above 1.
> Any hint ?

The problem is that in the binomial GLMM, the phenotypic variance varies 
according to the value of the intercept, which depends on included fixed 
effects etc.  There is an approximate heritability for this model 
described in Yazdi et al J. Dairy Sci. 85:1563­1577.

| 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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