What is the 'cutoff' value for Information Criteria like AIC and BIC?

[marcioadg]

When comparing two IC values, what is the cutoff value?

I have heard that it was 10, and also heard that it was 2...

[MohammadFayaz]

Hi,

Note : The difference is based on the AIC (BIC) of your desired model with the smallest AIC (BIC) in all your models.

For AIC , Page 30 : http://myweb.uiowa.edu/cavaaugh/ms_lec_2_ho.pdf

For BIC , Page 30 : http://myweb.uiowa.edu/cavaaugh/ms_lec_5_ho.pdf

[SteveDenham]

For AIC, there should be no "cutoff" value, in my opinion.  The smaller value (in SAS parlance) for two models reflects less information loss, as compared to the data generating process/model.  The loss compared to the model with the minimum AIC (AICmin) can be calculated as exp((AIC - AICmin)/2).  Thus even a small difference can indicate substantial information loss, e.g. a difference of 1.386 in AIC would represent a 50% loss.

Steve Denham

[MohammadFayaz]

Thank you SteveDenham.

I don't believe in "cutoff" for AIC as you say.But his question motivate me to search internet to find some rules. I don't use these rules. But if someone asks me have you ever heard about "cutoff" for AIC . I referred him to these pretensions. and then if he wants my opinion about using these "cutoff" , I tell him/her your invaluable example.

Thank you

[marcioadg]

SteveDenham and MohammadFayaz, thank you for your input. Do you have a reference for the exp((AIC - AICmin)/2) formula you gave? Thank you Marcio

[SteveDenham · Accepted solution]

See Burnham and Anderson's Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach (2nd. ed) (2002) from Springer-Verlag--Chapter 6, section 4.5, according to my notes.

Steve Denham

[marcioadg]

Thank you I will check. And how about when you have two exactly similar AIC and BIC between a linear and a quadratic model? Which one do we pick?

[SteveDenham]

Exactly similar?  That would be very coincidental.  I'd pick the model that I had the most solid biological reason for selecting, though, given this strange occurrence.

Steve Denham

[marcioadg]

Yes, Thank you Very much Steve