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I am working with complex models. I fitted two different models to my data. Then, I calculate the logliklihood function and the AIC and BIC values. I found that the log likelihood of the first models is higher than the other models, while the AIC and BIC corresponding to the model with higher log likelihood is larger than the other model. That is, AIC and BIC select the model with lower log likelihood. Would that acceptable or may something wrong?

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AIC and BIC are computed by two quantities. The log likelihood value is penalised by a quantity taking into account the number of parameters included in the model.
It might be that the model with higher likelihood includes "too many" covariates and the inclusion of those parameters does not increase the model estimate enough. Did you check also that difference?

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  • $\begingroup$ Yes that what I thought. But I really need to make sure that is acceptable mathematically. So, it is clear that if I have more densities then, the loglikelihood would be high than the model with low number of densities. However, that does not mean it is fit the data better than other model. $\endgroup$ – Silver_80 Jan 7 '18 at 11:31
  • $\begingroup$ Correct. Otherwise it would be enough to compare the log likelihood values. $\endgroup$ – Prunus avium Jan 7 '18 at 11:40

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