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
St?phane Chantepie