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

[chantepie at mnhn.fr]

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