[R] AIC and BIC in mixed effects model

[Ben Bolker]

Chuanjun Zhang <zhangchu <at> umkc.edu> writes:

> 
> Dear R Users:
> 
> I am trying to compare several structures of the within-patient covariance
> such as unstructured, Autoregressive, and spatial by using the MIXED effects
> model. Can AIC, BIC be negative ? If yes, then in what situations they may
> be negative.
> 

  This almost deserves to be a FAQ, although it's a statistical rather than an R
issue:

http://finzi.psych.upenn.edu/R/Rhelp02a/archive/46734.html
http://finzi.psych.upenn.edu/R/Rhelp02a/archive/108660.html

  The one-sentence answer is that since probability *densities* can be >1,
log-likelihood *densities* can be >0 and hence negative log-likelihoods can be
<0 (so AIC/BIC can also be <0).  However, there's a potentially larger issue
with using AICs for mixed models, which is that it's not always entirely clear
what the right number of degrees of freedom is for a random effect ...
 
  cheers
    Ben Bolker