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I have used AIC to do model selection before by just following the classic formula: AIC=2k-2L

But as far as I understand the absolute value of this score doesn't matter, only the relative score between 2 models. Then why bother the factor 2 for the number of parameters and log-likelihood. Do they matter at all? Am I missing something?

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"Actually, in his original paper (Akaike, 1973), he proposed using twice this (AIC(S) ≡ LS − dim(S)), to simplify some calculations involving chi-squared distributions. Many subsequent authors have since kept the factor of 2, which of course will not change which model is selected. Also, some authors define AIC as negative of this, and then minimize it; again, clearly the same thing."

This is in some the lecture notes of the professor Cosma Shalizi.

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  • $\begingroup$ So if I understand correctly "doubling" the AIC score is required if one wants to plug that score in a Chi2 test (I assume as the log-likelihood ratio follows approximately a Chi2 distribution). I still find it puzzling that people keep the factor 2 in the equation when computing DeltaAIC (difference in AIC scores). It's just confusing. $\endgroup$
    – baca
    Jun 27 at 14:04

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