[R-sig-ME] prior specification in MCMCglmm
Pierre B. de Villemereuil
bonamy at horus.ens.fr
Thu Apr 28 11:22:02 CEST 2011
The relationship between shape and informativeness is not that easy, I
think. First because "informativeness" is quite a difficult notion to
define. But also because everything depends on what you are looking for.
For example, a flat uniform prior on standard deviation would leads to
overestimation as stated in Gelman (2006). Besides, your prior on the
variance will be the uniform squared which is not flat anymore. So,
which one has to be flat ?
Or, another example, a weakly informative inverse-Gamma(0.001,0.001) on
an additive variance component (in an animal model) will leads to a huge
mass weight in 0 or 1 in the heritability scale, which could be (or not,
depending on the data) a problem.
Thus, I would say that one has to carefully look at the shape of the
prior (and to compare with the posterior to check the update), having in
mind what he wants to estime (the standard deviation ? the variance ?
heritability ?), but "the flatter, the better" is not always true in
every scale.
But considering the question of what is "nu" for MCMCglmm, it is hard to
answer not knowing how the distribution is really specified. If I refer
to the notation of the Wikipedia webpage (about inverse Wishart), it
looks like nu is the canonical "degree of freedom" (called m in the
webpage), but that V is defined like V=m*Psi (always refering to WP
notations). This stands for the univariate case (p=1), but what happens
for the multivariate ?
I think your should trust Jarrod on this subject, try the different
solutions Ned brought to us and see what happens !
Pierre.
Le 27/04/2011 18:40, Ned Dochtermann a écrit :
> That's my understanding as well. I think that the shape and
> "informativeness" of the prior are essentially conflated. For example, a
> flat prior would not be informing the posterior much so its shape and the
> amount of information imparted are related.
>
> Of course it is equally likely that I'm completely wrong on this.
>
> Ned
>
> --
> Ned Dochtermann
> Department of Biology
> University of Nevada, Reno
>
> ned.dochtermann at gmail.com
> http://wolfweb.unr.edu/homepage/mpeacock/Ned.Dochtermann/
> http://www.researcherid.com/rid/A-7146-2010
> --
>
>
> -----Original Message-----
> From: Celine Teplitsky [mailto:teplitsky at mnhn.fr]
> Sent: Wednesday, April 27, 2011 7:37 AM
> To: Ned Dochtermann
> Cc: r-sig-mixed-models at r-project.org; bonamy at horus.ens.fr
> Subject: Re: [R-sig-ME] prior specification in MCMCglmm
>
> Ned,
>
> thanks a lot, I'll try that and compare results with the different priors.
>
> What I just begin to understand is that nu is not really a degree of
> belief you can play with but a more specific parameter of a
> distribution, right?
>
> All the best
>
> Celine
>
>> There's a mistake in my email below.
>> The generalization of an inverse-gamma prior for multi-response models
>> should, I think, just be:
>> list(V=diag(x), nu=1.002)
>>
>> Sorry about that,
>> Ned
>>
>>
>>
>>
>> -----Original Message-----
>> From: Ned Dochtermann [mailto:ned.dochtermann at gmail.com]
>> Sent: Tuesday, April 26, 2011 1:12 PM
>> To: 'r-sig-mixed-models at r-project.org'; 'bonamy at horus.ens.fr'
>> Subject: Re: [R-sig-ME] prior specification in MCMCglmm
>>
>> Celine and Pierre,
>>
>> I too am still very unclear on priors however a month ago Jarrod replied
> to
>> some questions of mine regarding multi-response models with this:
>>
>> "From experience I find
>>
>> list(V=diag(2), nu=2, alpha.mu=c(0,0), alpha.V=diag(2)*a))
>>
>> where a is something large (e.g. 1000, depending on the scale of the
>> data) works well for the two standard deviations and the
>> correlation, in terms of informativeness.
>>
>> You can't use parameter expanded priors for the residual term yet,
>> so you will have to stick with the standard inverse-Wishart (or use
>> another program). Generally, data are highly informative for the residual
>> part so often the posterior is not very sensitive to the prior
>> specification. Nevertheless, you should check alternatives:
>>
>> V=diag(2), nu=1.002 gives the inverse-gamma prior for the variances
>> with shape=scale=0.001 V=diag(2)*1e-6, nu=3 is flat for the
> correlation
>> from -1 to 1"
>>
>> I think that this would generalize to G1=(list(V=diag(x), nu=1.00x)) for x
>> response variables for an inverse-gamma prior for G but I'm not entirely
>> positive that such is the case. I'm also not positive how to generalize
> the
>> flat prior (mainly would nu stay at three?), the first one I assume
>> generalizes to (V=diag(x), nu=x, alpha.mu=c(0,0...0x),alpha.V=diag(x)*a).
>>
>> The whole thread for this discussion starts here:
>> https://stat.ethz.ch/pipermail/r-sig-mixed-models/2011q1/005694.html
>>
>> The whole prior issue is still a mystery to me so I continue to be
>> uncomfortable with those approaches where they're necessary; nonetheless
> for
>> some data I'm analyzing they're basically necessary (e.g. multi-response
>> generalized mixed models). By and large the univariate analyses I've
>> conducted produce highly concordant results regardless of whether fitting
>> via REML, ML, Laplace or MCMC and regardless of priors for the latter.
> This
>> gives me a bit of confidence in the quantitative results and quite a bit
> of
>> confidence in the inferences. Unfortunately such comparisons aren't as
>> feasible (for me) with multi-response models.
>>
>> Ned
>>
>> --
>> Ned Dochtermann
>> Department of Biology
>> University of Nevada, Reno
>>
>> ned.dochtermann at gmail.com
>> http://wolfweb.unr.edu/homepage/mpeacock/Ned.Dochtermann/
>> http://www.researcherid.com/rid/A-7146-2010
>> --
>>
>> Message: 5
>> Date: Tue, 26 Apr 2011 09:41:58 +0200
>> From: "Pierre B. de Villemereuil"<bonamy at horus.ens.fr>
>> To: Celine Teplitsky<teplitsky at mnhn.fr>
>> Cc: r-sig-mixed-models at r-project.org
>> Subject: Re: [R-sig-ME] prior specification in MCMCglmm
>> Message-ID:<4DB67746.4000607 at horus.ens.fr>
>> Content-Type: text/plain
>>
>> Dear Ciline,
>>
>> I'm not very comfortable with covariance priors, but my guess is that,
>> is this case, you've got to really specify a inverse-Wishart as a prior.
>>
>> You should check into Hadfield's article introducing MCMCglmm, they use
>> something like V=diag(dimV)/4 and n=dimV. Why ? I have no idea. If your
>> data are not standardized, I don't think you should divide by 4 (but
>> then, you specify your prior as if your guess for variance components is
>> that they all equal 1), but for the rest...
>>
>> Sorry I can not help further. Maybe somebody else would be able to help
>> on this subject ?
>>
>> Pierre.
>>
>>
>> Le 26/04/2011 09:17, Celine Teplitsky a icrit :
>>> Dear Pierre,
>>>
>>> thanks a lot! It does help, but I will need time to fully understand
>>> the paper.
>>>
>>> Just one further question if I may, what prior would you use for a
>>> covariance then?
>>>
>>> Many thanks again,
>>>
>>> All the best
>>>
>>> Celine
>>>
>>>> Dear Ciline !
>>>>
>>>> One usual "non informative" prior on variance component is V=1, and
>>>> nu=0.002, which correspond to a inverse-Gamma(0.001,0.001). This is
>>>> usual, but that is not to say that it is really non informative.
>>>> Indeed, inverse-Gamma(e,e) is weakly informative, since the posterior
>>>> can depend on the choice of e.
>>>>
>>>> Concerning the WAMwiki suggestion to use the phenotypic variance to
>>>> set the prior, this quite not orthodox since no information coming
>>>> from your current dataset should be used to define the prior (but you
>>>> could use previous data to parametrize your prior).
>>>>
>>>> I would suggest you to refit your model considering V=1 and nu=0.002
>>>> as a (so-called) non informative prior. Other solutions exist like
>>>> using the parameter expansion and a chi2 distribution by setting
>>>> V=1,nu=1000,alpha.mu=0 and alpha.V=1, which is also weakly
>>>> informative (it has more weight in variance values less than 10).
>>>>
>>>> For more information about priors on variance component, and
>>>> parameter expansion, it would suggest you to read :
>>>>
>>>> 1. A. Gelman, + Prior distributions for variance parameters in
>>>> hierarchical models ;, /Bayesian analysis/ 1, n^o . 3 (2006):
>>>> 515--533.
>>>>
>>>> In the hope I'm helping.
>>>>
>>>> Pierre de Villemereuil.
>>>>
>>>>
>>>> Le 25/04/2011 13:26, Celine Teplitsky a icrit :
>>>>> Dear all,
>>>>>
>>>>> I realise that Jarrod is doing field work, but I'm really hoping
>>>>> someone can answer my question while he's not around.
>>>>>
>>>>> I am running animal models estimating covariances between life
>>>>> history traits, and I'm having trouble knowing which prior to use.
>>>>>
>>>>> Thing is, if I use a prior as described on the Wam wiki site with
>>>>> V=PhenotypicVar/4 (as I have 3 random effects + residual), I have
>>>>> very nice results, with some significant genetic correlations
>>>>> between some life history traits.
>>>>>
>>>>> However, one reviewer asked about prior sensitivity because CI were
>>>>> pretty large, so I went back to MCMCglmm course notes and saw that
>>>>> non informative prior were supposed to be V=diag(nbDimV)*0 and
>>>>> n=nbDimV-3. This led to an error message about G being ill
>>>>> conditioned, so I tried with diag(nbDimV)*0.001 and
>>>>> diag(nbDimV)*0.01 instead of diag(nbDimV)*0, and diag(nbDimV)*0.01
>>>>> worked... But then I have the posterior of additive genetic variance
>>>>> collapsing on 0 for some trait. So my guess would be that I should
>>>>> use those latest priors, and believe my nice results did not exist.
>>>>> But as Hadfield et al paper and the Wam wiki website do not
>>>>> recommend those priors, I am a bit confused. Could someone help me
>>>>> figure out what would be the right thing to do?
>>>>>
>>>>> All my apologies if this is a silly question, but I'm feeling a bit
>>>>> lost here
>>>>>
>>>>> Thanks a lot in advance
>>>>>
>>>>> Celine
>>>>>
>>>
>>> --
>>>
>>> Celine Teplitsky
>>> Dipartement Ecologie et Gestion de la Biodiversiti UMR 7204
>>> Uniti Conservation des Esphces, Restauration et Suivi des Populations
>>> Case Postale 51
>>> 55 rue Buffon 75005 Paris
>>>
>>> Webpage :http://www2.mnhn.fr/cersp/spip.php?rubrique96
>>> Fax : (33-1)-4079-3835
>>> Phone: (33-1)-4079-3443
>>
>> [[alternative HTML version deleted]]
>>
>>
>>
>> ------------------------------
>>
>> Message: 6
>> Date: Tue, 26 Apr 2011 11:53:02 +0200
>> From: peter dalgaard<PDalgd at gmail.com>
>> To: Junqian Gordon Xu<xjqian at gmail.com>
>> Cc: r-sig-mixed-models at r-project.org
>> Subject: Re: [R-sig-ME] interaction term in null hypothesis
>> Message-ID:<E1153437-757B-42E9-9A72-89EF9A368101 at gmail.com>
>> Content-Type: text/plain; charset="us-ascii"
>>
>>
>> On Apr 26, 2011, at 00:05 , Junqian Gordon Xu wrote:
>>
>>> I have a quick question for a simple model as below:
>>>
>>>> Fix + (1 | Rand) + (1 | Rand : Fix)
>>> Which one is the null hypothesis:
>>>
>>>> 1 + (1 | Rand)
>>> or
>>>
>>>> 1 + (1 | Rand) + (1 | Rand : Fix)
>>> To me the interaction term (1 | Rand : Fix) does not make much sense if
>>> no fixed effect term is present in the model, but I'm not sure.
>>>
>> It does make sense, at least sometimes. For one thing, such interactions
> are
>> often aliased to aspects of the experimental design; e.g., if you have
>> randomized different treatment to left side and the right side of test
>> subjects, then the random interaction is equivalent to the (random)
>> difference between the two sides within the same subject. Also, you could
>> conceivably have a kill-or-cure drug with positive effects for some and
>> negative effects for others, with the question being whether the total
>> effect is positive or negative.
>>
>>> Regards
>>> Gordon
>>>
>>> _______________________________________________
>>> R-sig-mixed-models at r-project.org mailing list
>>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>> --
>> Peter Dalgaard
>> Center for Statistics, Copenhagen Business School
>> Solbjerg Plads 3, 2000 Frederiksberg, Denmark
>> Phone: (+45)38153501
>> Email: pd.mes at cbs.dk Priv: PDalgd at gmail.com
>>
>>
>>
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