[R-sig-ME] glmer vs. MCMCglmm
Jarrod Hadfield
j.hadfield at ed.ac.uk
Thu Apr 2 13:02:43 CEST 2009
Hi,
As David suggested, the problem with binary data is that any residual
variance in the underlying probability cannot be observed, unlike
other types of data. For example, if data are generated according to
the process
y ~ binom(n=1, p=inv.logit(mu + e_i))
then the data look the same irrespective of the variance of the e's:
y1<-rbinom(1000, 1, inv.logit(rnorm(1000, 0, 1)))
y2<-rbinom(1000, 1, inv.logit(rnorm(1000, 0, 10)))
table(y1)
table(y2)
Because there is no information on VE (residual variance) we have to
make an assumption about its value. In terms of the fit of the model
to the data the choice of VE should make no difference because the
parameter is redundant. I think (if some one could clarify this that
would be great) that lmer fixes VE to zero, where with MCMCglmm the
user is free to fix VE at any value. Other than that I believe the
models should be identical. However, as VE approaches zero in MCMCglmm
mixing becomes problem, and actually when VE=0 the chain no longer
mixes at all.
With genetic models there are extra restrictions on the parameter
values which are not met when fitting a simple dam-sire model. Often
the parameter estimates lie within these restrictions, but with binary
data this is often not the case. The issue is that if genetic
variance (VA) exists, then you know apriori that VE in a dam-sire
model cannot be zero, because VE under this parameterisation actually
contains some VA (due to mendelian sampling variation). The animal
model, which you should be able to fit using MCMCglmm, not only
accounts for more complicated patterns of relatedness , but also
ensures that these restrictions are met. Even so, you still have no
information regarding the non-genetic VE and you have to fix it at
something. My guess is that there are certain things that are
invariant to the choice of VE (such a as the genetic correlation in
the Plodia example) but off-hand I don't know what they are. It may
also be possible to obtain post-analysis what the posterior
distribution of VA/fixed effects would be under a different assumption
about VE - but again I don't know the literature well enough to say.
One other worrying issue is that comparing DIC for different models
only seems valid if the same assumption regarding VE is used. Again,
any ideas/insights into this problem would be great.
Cheers,
Jarrod
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