[R] AIC value in lmer

[Douglas Bates]

On Fri, Nov 7, 2008 at 11:03 AM,  <ARNAUD_MOSNIER at uqar.qc.ca> wrote:
> Dear R Users,

> May be this message should be directy send to Douglas Bates ...
> I just want to know if I can use the AIC value given in the output of an lmer model to classify my logistic models.
> I heard that the AIC value given in GLIMMIX output (SAS) is false because it come from a calculation based on pseudo-likelyhood.
> Is it the same for lmer ???

I don't know about the situation with SAS.  The AIC value returned by
lmer is based on an approximation to the integral of the conditional
density of the random effects.  I had thought that I could evaluate
that conditional density from the sum of the deviance residuals for
the glm family but, given some recent discussion on the
R-SIG-Mixed-Models mailing list regarding the quasibinomial and
quasipoisson families, i am starting to doubt that.

So the quantity that is returned is based on something that is more
like the likelihood than is the pseudo-likelihood but may not be the
actual likelihood.

I do plan to change the value returned to be the likelihood for the
gaussian, binomial, poisson and Gamma families.  I don't know what to
do about the quasi families.  As far as I can see there isn't a
likelihood for those families because they don't represent a
probability distribution.

I am cc:ing the R-SIG-Mixed-Models mailing list on this reply.  I
suggest we move further discussion, if any, to that list.