AIC / BIC vs P-Values in lmer

I believe the recent discussion about AIC or p-values has missed a 
crucial practical issue.

The AIC statistic reported by a default call to lmer() has NOTHING to do 
with the choice of fixed effects.  lmer() uses reml to define the fit of 
a model.  REML (residual ML or restricted ML) is a log likelihood for a 
variance-covariance structure based on the residuals after fitting the 
fixed effects.  This has two consequences:
1) the AIC calculated from the reml lnL only informs you about the fit 
of the random effects model.
2) the reml AIC can only be compared between models with the same fixed 
effects.  Otherwise, the lnL is being calculated from different data 
(because different residuals with different X's).

This is a very common issue/problem.

use REML=F to force lmer() to calculate the full ML lnL.

Best wishes,
Philip Dixon