[R-sig-ME] Define prior in MCMCglmm

[Jarrod Hadfield]

Hi Maria,

random = ~us(1):subj_ID + us(fin_B):subj_ID  is the same as  
idh(1+finB):subj_ID and is not the same as (1 + fin_B|subj_ID) in lmer  
because the idh fixes the covariance between and intercepts and slopes  
to zero.  us(1+finB):subj_ID is equivalent to the lmer code.

Also, a prior of nu=2 (or nu=2.002) could have quite an influence on  
your posterior. V=diag(2) and nu=1.002 for the 2x2 case gives a  
marginal prior on the variances that is equivalent to an inverse gamma  
with shape and scale equal to 0.001. This prior used to be used a lot,  
but has some bad properties when values close to zero have support. I  
often use the parameter expanded prior:

list(V=diag(2), nu=2, alpha.mu=c(0,0), alpha.V=diag(2)*a)

where a is something large.

There is no difference between nu and n.

Cheers,

Jarrod

I meant (1 + fin_B|subj_ID), as indicated in glmer() (lme4 package).
> And this should be indicated in MCMCglmm() as random =  
> ~us(1):subj_ID + us(fin_B):subj_ID.


  Quoting Maria Paola Bissiri <Maria_Paola.Bissiri at tu-dresden.de> on  
Thu, 14 Nov 2013 15:06:26 +0000:

> Dear Szymek,
> thank you very much for your answer.
>
> Yes, the random effects were indicated wrongly in MCMCglmm! My  
> intention is of course to look at variance associated with subjects  
> (subj_ID).
> I meant (1 + fin_B|subj_ID), as indicated in glmer() (lme4 package).
> And this should be indicated in MCMCglmm() as random =  
> ~us(1):subj_ID + us(fin_B):subj_ID.
> Please, correct me if I am wrong.
>
> So the model runs with:
> k <- length(levels(fallmid$resp_X))
> I <- diag(k-1)
> J <- matrix(rep(1, (k-1)^2), c(k-1, k-1))
> prior <- list(R = list(fix = 1, V = 0.5 * (I+J), n = 2),
>                  G = list(G1 = list(V = diag(1), n = 2), G2 = list(V  
> = diag(2), n = 2)))
>
> fallmid.MCMCglmm <- MCMCglmm(resp_X ~ lang * ini_pch + lang * manner  
> + lang * fin_B,
>                              random = ~us(1):subj_ID + us(fin_B):subj_ID,
>                              family="categorical", data=fallmid,
>                              prior=prior
>                              )
>
> In your suggestion you indicate nu=2.002. What does "nu" mean? What  
> is the difference between nu and n? In the MCMCglmm manual and in  
> the tutorial they are both defined as "degrees of belief". What does  
> this mean?
>
> Kind regards,
> Maria Paola
>
>
>
>
>
>
>
> Zitat von Szymek Drobniak <geralttee at gmail.com>:
>
>> Dear Maria,
>>
>> I'm not sure what exactly you're trying to test with your model, but to
>> start with - your prior specification assumes 2 random effects, and your
>> model has only one (a structured covariance matrix with fin_B defined as a
>> random effect). This specification you've provided is similar to a random
>> intercept/slope model - but I can't see why you would like to fit it (most
>> importantly, you assumed that fin_B is both a fixed and random effect). If
>> your intention was to look at variance associated with subjects (subj_ID),
>> and you'd like to see if this variance is heterogeneous for different
>> levels of fin_B - you could fit:
>>
>> MCMCglmm(your_fixed_formula_here, random=~us(fin_B):subj_ID, ...)
>>
>> and the prior would be (assuming fin_B has 2 levels as you've said)
>>
>> list(R=list(V=1, fix=1), G=list(G1=list(V=diag(2),nu=2.002)))
>>
>> that's for start, then have a look at mcmc-series plots to see if it mixes
>> well and tweak your model further if necessary.
>>
>> Cheer
>> szymek
>
> -- 
> Dr. Maria Paola Bissiri
>
> TU Dresden
> Fakultät Elektrotechnik und Informationstechnik
> Institut für Akustik und Sprachkommunikation
> 01062 Dresden
>
> Barkhausen-Bau, Raum S54
> Helmholtzstraße 18
>
> Tel: +49 (0)351 463-34283
> Fax: +49 (0)351 463-37781
> E-Mail: Maria_Paola.Bissiri at tu-dresden.de
> http://wwwpub.zih.tu-dresden.de/~bissiri/index.htm
>
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