[R-sig-ME] MCMCglmm and prior specification

[Jarrod Hadfield]

Hi Cristina,

Sorry, yesterday I should have said

when V=0 & nu=-2 the MARGINAL posterior modes should be equal to the REML
estimates

not

when V=0 & nu=-2 the JOINT posterior modes should be equal to the REML
estimates

Cheers,

Jarrod
Sorry, yesterday I said
Quoting Jarrod Hadfield <j.hadfield at ed.ac.uk>:

> Dear Cristina,
>
> I am currently writing a better guide to MCMCglmm which deals more
> extensively with prior specifications - it should be ready soon.
>
> In your first prior you have fixed the residual variance to be V=1, so
> it's not surprising that this gives very different answers from models
> 2 and 3.
>
> Often variance components are sensitive to prior information, in part
> because the data may not contain much information but also because the
> inverse-Wishart prior used is not really flexible enough (again, I am
> working on this).
>
> The various improper priors often lead to numerical problems which
> precludes their use, but the resulting posterior does have some useful
> properties:
>
> when V=anything & nu=0 the joint posterior modes  should be equal to
> the ML estimate
> when V=0 & nu=-2 the joint posterior modes should be equal to the REML
> estimate (in practice you will have to use V=1e-6, or something small)
>
> A commonly used proper prior is V=1 & nu=0.002.  This is equivalent to
> the inverse gamma distribution with shape=scale=0.001. This was the
> "default" in WinBUGS for a while before Andrew Gelman showed why it
> shouldn't be - it can be informative if the variances are close to zero.
>
> Hope this helps,
>
> If anyone wants an unfinished copy of the MCMCglmm guide just email me.
>
> Jarod
>
>
>
> On 24 Nov 2009, at 16:42, ledonret at email.unc.edu wrote:
>
>> Dear all,
>>
>> I am trying to use the MCMCglmm package to create credibility   
>> intervals for random variables in my data. I'm having a bit of   
>> trouble though determining what the best prior to use for each   
>> model is, since the results seem to differ tremendously depending   
>> on which prior I am using, for instance, I've tried these three   
>> types of priors,
>>
>>> halfFam<-var(data$Family)/2
>>> prior1=list(R=list(V=1,n=1,fix=1),G=list(G1=list(V=1,n=1),G2=list(V=1,n=1)))
>>> prior2=list(R=list(V=1,n=1),G=list(G1=list(V=1,n=1),G2=list(V=1,n=1)))
>>> prior3=list(R=list(V=halfFam,n=1),G=list(G1=list(V=halfFam,n=1),G2=list(V=halfFam,n=1)))
>>
>> For the model,
>>> model<-MCMCglmm(Length~1,random=~Family+Rep,data=data,verbose=FALSE,prior=prior,burnin=10000,nitt=75000)
>>
>> Where the random factors are Family and Replicate.
>> From these priors, I get intervals for my Family effect,
>>
>>> HPDinterval(model1$VCV[,"Family"])
>>        lower     upper
>> var1 0.09660338 0.8888039
>>
>>> HPDinterval(model2$VCV[,"Family"])
>>       lower    upper
>> var1 0.1944570 2.120540
>>
>>> HPDinterval(model3$VCV[,"Family"])
>>       lower    upper
>> var1 0.2099238 1.529794
>>
>>
>> I feel bad that I don't understand better how to specify the   
>> components of these priors, but from what I understand, the model   
>> should return similar values even if the priors are very different.  
>>  I've looked through the vignette thoroughly, but didn't get a  
>> sense  of what I was supposed to do if alternate priors returned  
>> different  answers. I'm not sure whether this is telling me that  
>> all the  information is coming from my priors (and there is, in  
>> fact, no  information in the data), or I am just incorrectly  
>> specifying my  priors.
>>
>> Any insight would be very much appreciated! Happy holidays,
>>
>> Cristina Ledon-Rettig
>> UNC-Chapel Hill
>>
>> *I am using lme4 version 0.99375-28 with Mac OS X version 10.5
>>
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>>
>
>
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The University of Edinburgh is a charitable body, registered in
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