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Tom: That's a good question. AIC, as i'm sure you know, is usually calculated as 2k-2ln(L), where k is the number of free parameters in the model, and L is the log-likelihood of the model. The goal of AIC--and the reason one normally tries to select a model with minimal AIC--is to minimize what's referred to as the Kullback-Leibler distance between the distribution of your data's density from the theoretical "true" theoretical density as defined by the model. More concisely, the AIC is an index of the amount of information regarding your data that is lost when your model is used to describe it. To get back to your question, I can't say without a little more information why the AIC's your referring to are negative (but perhaps it's an issue of using the log-likelihood instead of the negative log- likelihood), but my first instinct is that it doesn't matter. I would go with the AIC that is closest to zero. I hope that helps. Kyle H. Ambert Graduate Student, Dept. Behavioral Neuroscience Oregon Health & Science University ambertk at ohsu.edu On Aug 3, 2007, at 8:41 AM, Tom Willems wrote:> Dear fellow R-ussers, > I have a question about the Akaike Information Criterion in the R > output. > Normally you would want it to be as small as possible, yet when i > check up > the information in my study books, the AIC is usually displayed as a > negative number. In the exercises it is given as " - AIC ". > R displays it as a positive number, does this mean that a large "AIC" > gives a small " - AIC ", so the bigger the better? > > > Kind regards, > Tom. > > > > > Tom Willems > CODA-CERVA-VAR > Department of Virology > Epizootic Diseases Section > Groeselenberg 99 > B-1180 Ukkel > > Tel.: +32 2 3790522 > Fax: +32 2 3790666 > E-mail: towil at var.fgov.be > > www.var.fgov.be > > > > > Disclaimer: click here > [[alternative HTML version deleted]] > > ______________________________________________ > R-help at stat.math.ethz.ch mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting- > guide.html > and provide commented, minimal, self-contained, reproducible code. >
Tom Willems <Tom.Willems <at> var.fgov.be> writes:> I have a question about the Akaike Information Criterion in the R > output. > Normally you would want it to be as small as possible, yet when i check up > the information in my study books, the AIC is usually displayed as a > negative number. In the exercises it is given as " - AIC ". > R displays it as a positive number, does this mean that a large "AIC" > gives a small " - AIC ", so the bigger the better? >I don't know about your books, but confirm that smaller AIC is better. AIC is usually positive (likelihood is between 0 and 1, therefore log-likelihood is negative, therefore -2L + 2k is positive), although continuous probability densities or neglected normalization coefficients can lead to negative AICs -- but smaller (more negative, if AIC<0) is still better. Ben Bolker
Ah. Very good point. I stand corrected. ---Kyle.>>> ted.harding at nessie.mcc.ac.uk 08/03/07 10:32 AM >>>On 03-Aug-07 16:42:33, Kyle. wrote:> Tom: > > That's a good question. AIC, as i'm sure you know, is usually > calculated as 2k-2ln(L), where k is the number of free parameters in > the model, and L is the log-likelihood of the model. The goal of > AIC--and the reason one normally tries to select a model with minimal> AIC--is to minimize what's referred to as the Kullback-Leibler > distance between the distribution of your data's density from the > theoretical "true" theoretical density as defined by the model. More> concisely, the AIC is an index of the amount of information regarding> your data that is lost when your model is used to describe it. To > get back to your question, I can't say without a little more > information why the AIC's your referring to are negative (but perhaps> it's an issue of using the log-likelihood instead of the negative log-> likelihood), but my first instinct is that it doesn't matter. I > would go with the AIC that is closest to zero. I hope that helps.That could be wrong! Don't forget that ln(L) is indeterminate to within an additive constant (for given data), so one man's negative AIC could be another mans positive AIC -- but if each compared their AICs with different models (the same different models for each) then they should get the same *difference* of AIC. The correct approach is to compare AICs on the basis of algebraic difference: AIC1 - AIC2 in comparing Model1 with Model2. If this is positive then Model2 is better than Model1 (on the AIC criterion). Taking "the AIC that is closest to zero" would be the wrong way round for negative AICs. Ted.> On Aug 3, 2007, at 8:41 AM, Tom Willems wrote: > >> Dear fellow R-ussers, >> I have a question about the Akaike Information Criterion in the R >> output. >> Normally you would want it to be as small as possible, yet when i >> check up the information in my study books, the AIC is usually >> displayed as a negative number. In the exercises it is given as >> " - AIC ". >> R displays it as a positive number, does this mean that a large "AIC" >> gives a small " - AIC ", so the bigger the better? >> >> Kind regards, >> Tom. >> >> Tom Willems >> CODA-CERVA-VAR >> Department of Virology >> Epizootic Diseases Section >> Groeselenberg 99 >> B-1180 Ukkel >> >> Tel.: +32 2 3790522 >> Fax: +32 2 3790666 >> E-mail: towil at var.fgov.be >> >> www.var.fgov.be-------------------------------------------------------------------- E-Mail: (Ted Harding) <ted.harding at nessie.mcc.ac.uk> Fax-to-email: +44 (0)870 094 0861 Date: 03-Aug-07 Time: 18:31:51 ------------------------------ XFMail ------------------------------ ______________________________________________ R-help at stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
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