bayes factors for MCMCglmm

Mikhail Matz <matz at ...> writes:

 Hello - is it possible to calculate hayes factors for MCMCglmm
objects, to compare alternative models?  Mikhail

Well, MCMCglmm gives you a posterior sample for the deviance, so
in principle you could calculate the harmonic mean of the likelihood,
e.g.

data(PlodiaPO)  
model1<-MCMCglmm(PO~1, random=~FSfamily, data=PlodiaPO, verbose=FALSE)

likchain <- exp(-model1$Deviance/2)
1/mean(1/likchain)

  these are ridiculously big numbers -- that may have something
to do with the way the deviance is scaled.

  However, harmonic means are known to be really, really
dodgy estimates of the Bayes factor -- see e.g.

http://scholarworks.umass.edu/cgi/viewcontent.cgi?
   article=1107&context=astro_faculty_pubs
(warning, broken URL)

  Perhaps someone else will contribute something more useful.
  You could also use DIC to compare models, although it has
its own issues ...

Hi,

The fact that the deviance is not calculated after marginalising the  
random effects may also be an issue for Bayes factors, as it can be  
with DIC. But not sure.

Cheers,

Jarrod


Quoting Ben Bolker <bbolker at gmail.com> on Tue, 28 Aug 2012 02:43:23  
+0000 (UTC):

Mikhail Matz <matz at ...> writes:

 Hello - is it possible to calculate hayes factors for MCMCglmm
objects, to compare alternative models?  Mikhail

Well, MCMCglmm gives you a posterior sample for the deviance, so
in principle you could calculate the harmonic mean of the likelihood,
e.g.

data(PlodiaPO)
model1<-MCMCglmm(PO~1, random=~FSfamily, data=PlodiaPO, verbose=FALSE)

likchain <- exp(-model1$Deviance/2)
1/mean(1/likchain)

  these are ridiculously big numbers -- that may have something
to do with the way the deviance is scaled.

  However, harmonic means are known to be really, really
dodgy estimates of the Bayes factor -- see e.g.

http://scholarworks.umass.edu/cgi/viewcontent.cgi?
   article=1107&context=astro_faculty_pubs
(warning, broken URL)

  Perhaps someone else will contribute something more useful.
  You could also use DIC to compare models, although it has
its own issues ...

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