Solved – Calculating the AICc and BIC with RSS instead of likelihood

aicbicmodel selection

I have found here that that the akaike information criteria, corrected for small sample sizes is:

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where:

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And that the likelihood can be replaced with residual sum of squares (RSS) divided by n, the sample size.

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so that

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My question is if the likelihood function and RSS are equivalent if the RSS is first divided by the sample size, can I also do the same with the Bayesian information criteria? i.e.

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Also, I want to be able to reference this information in a paper (and unfortunately the link above doesn't cut it). Its easy enough to find these equations but harder to find somewhere that describes why the likelihood function is equal to the RSS divided by n. Could somebody describe why this is the case or point me to a source?

Best Answer

I do not have a direct answer in this question, but let me underline that this AIC equation is not proper. As given in wikipedia, the AIC formula with RSS (instead of likelihood) is:

$AIC = 2k + n\cdot ln(\frac{RSS}{n})$.

This could lead to major modelling problems.

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