# If the log-likelihood is negative, should we choose it? - model comparison

I am doing linear mixed models using lme4 and this is the results of model comparison:

> anova(lmer5,lmer6,lmer32)

Df   AIC   BIC logLik   Chisq Chi Df Pr(>Chisq)
lmer32  9 43172 43226 -21577
lmer6  21 43190 43315 -21574  6.3081     12     0.8998
lmer5  26 43162 43317 -21555 37.9971      5  3.778e-07 ***


As you can see, the results show that one model is significantly better than the others and normally I will choose model with smallest logLik. However in this result, the logLik is negative. Do you think it is a good idea to choose model from logLik in this case, or should I choose it from AIC or BIC instead.

As no conclusion whether AIC is better than BIC, I am confused which one I should choose. What do you think?

• Why do you think the AIC and BIC don't agree? How does sample size impact AIC and BIC? Is one better than the other? Should you compare models without taking DF into account? Feb 25, 2014 at 17:34
• Are you sure you mean the smallest loglikelihood?
– Momo
Feb 25, 2014 at 17:38
• From an article, it uses the model with highest adjusted R-squared. Is it that the adjusted R-squared value is derived from the logLik^2? Feb 25, 2014 at 18:02
• Right. I think I got a grip then. Thank you, Charles and everyone. Feb 25, 2014 at 19:46
• Whether log-likelihood is negative is irrelevant to any of the considerations in your question. You could (legtimately) add a million to all the log-likelihood values (making them all positive) without changing anything of consequence in a comparison of log-likelihoods. Feb 25, 2014 at 23:11