Bonnie asks:
> Iâm getting conflicting answers to a question and am hoping you could help.
>
> When using the Akaike Information Criterion (AIC), am I looking for the
> smallest number or the smallest absolute number?
>
> For example, I have two models.
>
> (-2 log likelihood) + (2k)
>
> log likelihood k AIC
>
> 532.5052 16 -1033.0104
> 509.8392 58 -903.6784
>
> the difference between the two is great, but which is better?
> -1033.0104 is the smallest, but -903.6784 is the smallest absolute value.
>
> I wonât say which model I LIKE better. =)
If the values are close, then it's a more a matter of preference and what
your goals in creating the model are than absolute values. It's important to
remember that the AIC was developed as an engineering metric for black-box
models,
a mathematical expression of Ockham's Razor ("Pluralitas non est ponenda sine
neccesitate," -- don't add in things unnecessarily).
[a "black box" model is just that, a box with an input socket and a matching
output on the other side, but you have no idea of what's inside it or how it's
constructed internally. All you care about is its stimulus/response behavior.]
The two values of the AIC
(-2 log likelihood) + (2k)
measure the goodness of fit of the model and its complexity, respectively.
In engineering, more complexity means more components and thus generally more
unreliability over the long term, but if goodness of fit in the model is of
paramount importance, you may well accept a higher level of complexity in order
to obtain a very high quality prediction. On the other hand, if reliability,
and thus low parts count, is maximally important to your application,
especially if prediction to only "good enough for government work" standards is
all
that you need, you will work to primarily minimize the model's complexity.
These choices of course presume that you have multiple minima in your AIC
values. It is entirely possible that the optimization surface is a simple bowl
however with a single point of global optimality. If that's so, and the true
costs of additional complexity are accurately represented in the second term,
then you would always choose the lowest absolute value.
Wirt Atmar
