The sign of the AIC tells you absolutely nothing about ill conditioned parameters or whether the model is suitable or not. For example, in a linear regression case, if the AIC is positive, you can make it negative (or vice versa) just by multiplying every observation on the dependent variable by the same number. That obviously does not change the characteristics of the model. Like other such measures, AIC is only useful when it is used to compare one model to a different model that seeks to explain the same data (variable). By itself, it is meaningless.

I think many a times it is negative.

The log likelihood is guaranteed to be negative if it applies to a discrete choice model. In other cases, including your linear random effects regression, it can take either sign and any magnitude. (For the linear regression it is a function of the log of the average squared residual, which obviously can be greater than or less than 1.) As such, the AIC, computed by the formula you show, can be negative or positive.

As you can see from the formula there is nothing that constrains AIC or any other criterion to have a fixed sign. In general the smaller it is thr better.

However we should note that AIC is not asymptotically consistent unlike other criteria such as Hannan-Quinn or BIC. And consequently it is thought to result in somewhat over parameterized models.

The model or parameter must be ill conditioned if there is a non positive situation

Yes it can be non positive and the its non positive magnitude translates that the applied econometric model is not suitable to conclude the findings..

It may be having some specification issue

The sign of the AIC tells you absolutely nothing about ill conditioned parameters or whether the model is suitable or not. For example, in a linear regression case, if the AIC is positive, you can make it negative (or vice versa) just by multiplying every observation on the dependent variable by the same number. That obviously does not change the characteristics of the model. Like other such measures, AIC is only useful when it is used to compare one model to a different model that seeks to explain the same data (variable). By itself, it is meaningless.

I personally don't see what the big deal about negative is. It's all about balancing parameters and fit. (a more sophisticated adj R-sqr). Lower is better. No specification issue when it's negative--it is just fitting better. Big deal. It's the relative magnitude that matters anyway---how do nonnested models relate in terms of fit vs number of parameters?

As i know, its doesnt matter negative or positive...we can take any sign...bt it should be smallest value

Yes, AIC is may take any sign. It more appropriate when used for choosing among econometric models.

I agree nick.. and was explaining the same that its a matter of fitting better.

Thanks a lot for your answers! They have been very useful

Yes, just select the most negative.....lowest is best. Here is a paper where it is negative and demonstrated in FE and RE models: http://www.engr.wisc.edu/cee/faculty/russell_jeffrey/002.pdf

AIC may be either positive or negative. It is more appropriate when used for choosing among econometric models, we prefer model with lowest AIC value.

What really maters is that the AIC be as small as possible in number and regardless of its sign. Thus it is not of much importance if it is positive or negative.

I know this is an old question, but because it came up in my search for information on AIC, I suppose it will also come up when other people search this subject, and I found a good way to get to understand the AIC, so I thought I ought to share (please correct me if I am wrong! I am still new to the subject).

It really helps to insert your AIC into this formula to understand it:

exp((AIC1−AIC2)/2)

This will result in the probability of the model with AIC2 to minimize information loss compared to the model with AIC1.

example:

AIC1 = 100; AIC2 = 110

exp((100-110)/2) = 0.0067

The second model is 0.0067 times as probable as the first model to minimize information loss.

This is of cause also useful for looking at models with negative AIC values.

e.g.: exp(((-100)-110)/2) = 2.50e-46

Short of digging into the math, I'm wondering how to treat the general rule here of finding the "lowest" AIC when we're dealing with negative values. Do we want the smallest AIC in absolute values (i.e., the AIC closest to zero) or the lowest with respect to the negative sign (i.e., -400 is better than -300, ceteris paribus)? 

Ok, so now I have read up on the AIC value...

It is a measure of information loss, and therefore you would want as little information loss in your model as possible. 

Further more it is only meaningful to look at AIC when comparing models!

But to answer your question, the lower the AIC the better, and a negative AIC indicates a lower degree of information loss than does a positive (this is also seen if you use the calculations I showed in the above answer, comparing AICs).

If you want some more detailed information try the link.

https://books.google.dk/books?id=ObUcBQAAQBAJ&lpg=PA402&ots=-efTnJkDZp&dq=akaike%20information%20criterion%20absolute%20value&pg=PA402#v=onepage&q=akaike%20information%20criterion%20absolute%20value&f=false

The values of penalty functions like Aic, Bic etc totally depend upon the maximized value of likelihood function (L),  which can be positive or negative. If the value of L is negative your Aic value will be positive and vice versa. 

minimum value is the best 

Hello. Can I use AIC for Binary choice models ? I am using Recursive multivariate probit model, where I have 3 correlated models, with endogenous variables in the second and third model. So, in my first model i have total of 14 variables, in second 15 and third 16. If i use AIC, how many parameters should I include in the AIC formula?

is it normal if i obtain negative AIC values?

Maisarah Afiqah Nasaruddin: yes, they can be negative too.. Look at some of the above answers and you can get some more information to undestand AIC values.

So a model with an AIC of -2.21 is better than a model with an AIC of 1.07, correct?

Yes

Thank you!

Does aic negative always for possion regression?