[R-sig-ME] MCMCglmm : Difference in additive genetic variance estimated in univariate vs bivariate models

[Jarrod Hadfield]

Hi Stephane,

If I am worried about prior influence and my model is multi-trait  
Gaussian I often run it through ASReml as a check.  Generally I find  
parameter expanded priors to be weaker than the inverse-Wishart and  
usually use them. Unfortunately I haven't seen much work done  
regarding their properties for covariance matrices. However, having

V=diag(n), nu=n, alpha.mu=c(0,0), alpha.V=diag(n)*s

where n is the dimension of the matrix and s a scale parameter  
(assuming the traits are on the same scale) seems to work well under  
at least some circumstances. Even with low replication the posterior  
modes are close to their REML estimates, and if one of the variance is  
close to zero then the posterior for the correlation is close to being  
uniform on the -1/1 interval, as you would hope  - approximate  
standard errors for this correlation obtained from REML analyses often  
seem to be anti-conservative.

Cheers,

Jarrod





Quoting Stephane Chantepie <chantepie at mnhn.fr> on Thu, 19 Jul 2012  
17:20:24 +0200:

> Hi Jarrod and all other,
>
> You said "your posterior is just reflecting your prior" : I was  
> thinking about
> this issue but how can I test it? The V I used is V=(Phenotypic variance/2)=
> 0.47 so it is bigger than the posterior mode. I have tried to used  
> V=1 but the
> Va posterior results remains the same (Va=0.10 for the univariate model
> spz_9).
>
> For the bivariate model c(spz_9,spz_5) I have kept the same V=(Phenotypic
> variance/2)but nu=2.
> To answer your question "if nu=1 then V*nu/(nu-1) is ..."  V*nu/0 so +∞ or -∞
> ;-)
>
> Just to give you an idea of the my posteriors:
>
> The Va posterior mode resulting from the spz_9  univariate model hit the 0
> (http://ubuntuone.com/2IGcmcdqkjcVQCdZgvMhnP) whereas the Va posterior mode
> resulting from the (spz_9,spz_5) bivariate model seems to be better shaped(at
> the top http://ubuntuone.com/3PaBOJ5dF6kDIhV6ahPnlM).
>
> To conclude, the estimation of Va with bivariate models is biologically
> consistent with senescence theories while the Va estimated with univariate
> model is not. So : Do do you think that I could use bivariate  
> results or it is
> better to consider that I do not have enought information?
>
> Thank a lot for your help
>
> all the best
>
> stephane
>
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