[R-sig-ME] Accuracy of Va estimates using univariate versus multivariate animal model

[Jarrod Hadfield]

Dear Stéphane,

Va estimates may change between univariate and multivariate models for  
(at least) three reasons:

1/ The priors may have different effects, even if you have the same  
marginal priors for each variance. It is probably easier to understand  
this with a simpler example: Imagine I draw 100 numbers from a unit  
normal (mean zero, variance one), and fitted a model in which I placed  
a strong prior on the mean that conflicted with the true mean (lets  
say I put a prior point mass on a mean of 1) but used a flat improper  
prior for the variance. The posterior for the variance would give  
support for higher values than if a weaker prior on the mean was  
given. This happens because deviations are being calculated from a  
mean of one, rather than a mean closer to the data-driven value of  
zero. The marginal prior for the variance is flat and does not alert  
us to the fact that the prior on the mean may be informative for the  
variance.

2/ As you point out, if there is selective drop-out then Va in later  
age-classes may be smaller in the univariate model then the  
multivariate model. The multivariate model accounts for selection  
(under some conditions). The multivariate estimates are therefore  
better because they tell you what Va would have been had there been no  
selection. Va in the univariate models will change as the strength and  
pattern of selection change.

3/ (Possibly) Imagine a trait with h^2=1 and a trait h^2=0.1, and the  
genetic correlation is 1. Up to proportionality you know the breeding  
values for the second trait perfectly; they are the phenotypic values  
of the first trait. In a univariate analysis it would be much more  
difficult to predict the breeding values because of all the residual  
noise. So, the precision of the breeding value predictions clearly  
goes up in a multivariate model. However, I'm not sure whether this  
effect is also true for Va of the second trait, since it is the  
coefficient of proportionality for breeding value prediction. Possibly  
not, but I would have to check.

Cheers,

Jarrod











Quoting chantepie at mnhn.fr on Thu, 17 Jul 2014 14:03:50 +0200:

> Dear all,
>
> I have a question concerning the interpretation of Va estimate using  
> univariate versus the bivariate animal models.
>
> Indeed, I am interested to understand the age-related variation of  
> the additive genetic variance. For this, I made an analysis with  
> different age classes using univariate models for each age class. I  
> also tried to run a multivariate model with my different age classes  
> (9 in total). Nevertheless, even if the multivariate model can be  
> written and runs, the time needed to reach its converenge is greater  
> than 1 year.
>
> I'd like to know if it is better to estimate the Va of an age-class  
> with a multivariate animal model than with a univariate one and why?
>
> My view of the problem :
>
> I understand that with univariate models the ages classes are  
> considered as separate traits while in fact, the age classes are not  
> independent because the same individuals are found in different ages  
> classes. However, I do not really see the problem that univariate  
> model can generate on the estimates of Va and therefore in the  
> interpretation of results (as suggest a reviewer).
>
> When I realized bivariate models between two ages-classes where  
> there is a lot of information in each of the age-classes , the  
> variance of traits remains the same compared with univariate models.  
> However, when one of the age classes has less information (basically  
> with the old ages eg classes), the variance  estimates may be  
> different for this age clases (always in comparison with univariate  
> models). Note that all models were run with expanded parameters  
> priors.
>
> I do not understand how the variance can change between two models  
> (univariate and bivariate). In bivariate models, it is like Va  
> estimate of an age class depends on the estimate of the covariance  
> between age classes. For me, variance ??is calculated  independently  
> from covariance (for example if var(x1)=cov(x1,x1), there is no use  
> of cov(x1,x2)). After a long search, I did not find the line in the  
> MCMCglmm function that could answer my question.
> I was wondering if the  covariance properties between age classes  
> were used to extrapolate missing points and thus refine the Va  
> estimates. If this is the case, the variances calculated using  
> multivariate models would be suceptible to estimate a biased Va for  
> age classes which contain a large number of empty rows.
>
> So if I go back to my questions :
>
> Are there any constraints when estimating variance with univariate  
> models compared with multivariate models? With univariate models,  
> the estimated variances are they less 'real' than a multivariate  
> model?
>
> In bivariate models, Is there a dependency between the Va estimate  
> of an age-class and the covariance between this age class and  
> another one?
>
> Thank in advance for your reply
>
> Stéphane Chantepie
>
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>
>



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