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11-30-2012 02:26 PM

According with Akaike 1974 and many textbooks the best AIC is the minor value. However, I am still not clear what happen with the negative values. Some said that the minor value (the more negative value) is the best. However, other said that the value closer to zero, this means the minor absolute value, is the best.

Someone could help me with this doubt? Will be great if you could give a quote. I only have found answers in both directions in blogs

Thanks,

Juan

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Solution

12-01-2012
03:09 PM

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12-01-2012 03:09 PM

The magnitude of AIC for a specific model is less of interest than the comparison of AICs for two or more models because AIC is usually used in the context of comparing models, not as an absolute criterion in itself. Thus, your question is irrelevant in this context because it asks about a "best" AIC value. The usual "rule" for comparing two or more models is to choose the one with the minimum AIC value. This minimum value may or may not be negative. For example, in multiple linear regression, the AIC value is estimated as

N*ln(error-sum-of-squares/N) + 2*(number of independent variable parameters including the intercept term),

where N=the number of observations.

If a model were so good that it (almost) perfectly predicted the dependent variable, the error-sum-of squares would approach zero,

and the natural logarithm of this value and the AIC would approach negative infinity. Thus, the better the independent variables of this linear regression model are in predicting the dependent variable, the more negative the AIC becomes. However, this "asymptotic" behavior is less important to the usefulness of AIC than the comparison of the AIC values of different models. Smaller AIC values are better when comparing two or more models.

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Solution

12-01-2012
03:09 PM

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12-01-2012 03:09 PM

The magnitude of AIC for a specific model is less of interest than the comparison of AICs for two or more models because AIC is usually used in the context of comparing models, not as an absolute criterion in itself. Thus, your question is irrelevant in this context because it asks about a "best" AIC value. The usual "rule" for comparing two or more models is to choose the one with the minimum AIC value. This minimum value may or may not be negative. For example, in multiple linear regression, the AIC value is estimated as

N*ln(error-sum-of-squares/N) + 2*(number of independent variable parameters including the intercept term),

where N=the number of observations.

If a model were so good that it (almost) perfectly predicted the dependent variable, the error-sum-of squares would approach zero,

and the natural logarithm of this value and the AIC would approach negative infinity. Thus, the better the independent variables of this linear regression model are in predicting the dependent variable, the more negative the AIC becomes. However, this "asymptotic" behavior is less important to the usefulness of AIC than the comparison of the AIC values of different models. Smaller AIC values are better when comparing two or more models.

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12-01-2012 05:09 PM

Thanks for your response. May be my question was not too clear.

Yes, understand there is not a best AIC value. I was asking if the have two or more negative AIC, What model I need to choice?

Following your example I understand that with the more negative AIC.

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12-03-2012 07:58 AM

1zmm has given all you need: Smaller IC values are better when comparing models. It makes no difference that the actual value is negative. Suppose the first model you are considering has an AIC of -1000, while the second has an AIC of -950. The first model has the smaller AIC, and fits your data better.

Steve Denham

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12-03-2012 11:29 AM

Thanks Steve, I forgot to close the question