[R-sig-ME] bayes factors for MCMCglmm

[Ben Bolker]

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 ...