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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?

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    $\begingroup$ 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? $\endgroup$ – charles Feb 25 '14 at 17:34
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    $\begingroup$ Are you sure you mean the smallest loglikelihood? $\endgroup$ – Momo Feb 25 '14 at 17:38
  • $\begingroup$ 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? $\endgroup$ – user3288202 Feb 25 '14 at 18:02
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    $\begingroup$ Right. I think I got a grip then. Thank you, Charles and everyone. $\endgroup$ – user3288202 Feb 25 '14 at 19:46
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    $\begingroup$ 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. $\endgroup$ – Glen_b -Reinstate Monica Feb 25 '14 at 23:11
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check https://mailman.ucsd.edu/pipermail/ling-r-lang-l/2011-August/000282.html you want to have large (i.e. in direction of positive infinity) logLik and small AIC/BIC (i.e. in direction of negative infinity)

also caution BIC is only valid for comparisons of not nested models (see https://en.wikipedia.org/wiki/Bayesian_information_criterion), if models are nested orient with AIC alone, if models are not nested you can orient for both AIC and BIC

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  • $\begingroup$ I am not sure how this answers the question. It seem to be more like advice and maybe not all accurate. $\endgroup$ – Michael R. Chernick May 12 '17 at 20:22
  • $\begingroup$ "large (i.e. in direction of positive infinity) logLik" sounds like exactly the opposite of what should be done: it corresponds to minimizing the likelihood. Could you clarify what you mean by that? $\endgroup$ – whuber May 12 '17 at 21:38

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