[R] AIC and BIC in mixed effects model

Ben Bolker bolker at ufl.edu
Fri Dec 28 23:02:41 CET 2007

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


  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 ...
    Ben Bolker

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