# negative AIC ?

#### helenekuo

##### New Member
Hello,

I ran model selection by delta AIC but encountered most of the AIC as negative.
(R package AICcmodavg and stat : AIC)

As reviewed by reference,
AIC is defined as

-2*log-likelihood + k*npar,
where npar represents the number of parameters in the fitted model, and k = 2 for the usual AIC, or k = \log(n) (n the number of observations)

I would like to ask under what condition will AIC become negative ?
How to test if my case satisfy the condition?
(Is it possible to have a log-likelihood over 1 ?)

Thank you

##### Ninja say what!?!
AIC can only be negative if the log-likelihood value is positive. I have yet to see that happen.

hmmmm....thinking about it. I found it plausible for the log-likelihood to be positive. Searching around, I found

"For discrete outcomes, the log likelihood is the log of a probability, so it is always negative. For continuous outcomes, the log likelihood is the log of a density. Since density functions can be greater than 1 (cf. the normal density at 0), the log likelihood can be positive or negative.