[R-sig-ME] AIC and BIC with ML and REML

[Gorjanc Gregor]

> In a way this question relates to the earlier discussion on whether to
> regard the random effects as parameters or as unobserved random
> variables.  The difference between -2 * l + 2 * p and -2 * l + 2 * (p
> + q) can be considered to be a question of how many parameters there
> are in the model.  In particular, do the random effects count as
> parameters?  I had an interesting discussion with Georges Monette
> about this a few days ago and both of us feel the saying the random
> effects don't affect the parameter count is underestimating the
> complexity of the model but saying they should add q to the number of
> parameters is overestimating the complexity.

Thanks for this comment. I will take this as a yes to: "Are there are several
definitions of AIC and BIC lurking around?".

DIC "solves" the issue of effective number of parameters to some extent
though it also has its own problems

http://www.mrc-bsu.cam.ac.uk/bugs/winbugs/dicpage.shtml

> I don't know a good answer to the question of how to "count" the
> number of parameters in a mixed model (but I also don't feel that AIC
> or BIC should be taken too seriously - these quantities are, at best,
> a guide for model comparisons).

Sure.

gg