[R-lang] Positive and negative logLik and BIC in model comparison (lmer)

[Anja Arnhold]

Dear list,

 I have had a problem with model comparison for several months, so now
 I finally worked up my courage to ask for your help and hope that you
 can settle the question.

 I have frequently encountered positive logLik values and now heard
 that this might be due to bug in the lmer function. However, I also
 recently found Douglas Bates stating that "a positive log-likelihood
 is acceptable in a model for a continuous response" in an S-list.
 Positive logLiks appear in Baayen's 2008 introductory book, always
 together with negative AIC and BIC. He does not seem to treat them as
 erroneous. Instead, if I understood correctly, he chooses the model
 with more negative AIC/BIC (smaller value) and more positive logLik
 (larger value) as the better model in these comparisons.
 So did I get it right and is this the way to go or is there a bug that
 inverts the polarity of the numbers?

 As second question: Is there a general rule of thumb for cases when
 AIC and BIC point into different directions? Does it depend on the
 data set? Or is it a matter of taste how much one wants to avoid
 overfitting? Should one trust the value that agrees with the logLik?

 Many thanks in advance
Anja