Typical values of AIC that I have seen for logistic models are in thousands, at least hundreds. e.g. On http://www.r-bloggers.com/how-to-perform-a-logistic-regression-in-r/ the AIC is 727.39
While it is always said that AIC should be used only to compare models, I wanted to understand what a particular AIC value means. As per the formula, $AIC= -2 \log(L)+ 2K$
Where, L = maximum likelihood from the MLE estimator, K is number of parameters
In the above example, K =8
so, with simple arithmatic:
727.9 = -2*log(L)+ 2*8 Hence, 711.39 = -2*log(L) Hence, log (L)= 711.39/-2 = -355.695 Hence, L = exp(-355.695) = 3.3391E-155
So, if my understanding is correct, this is the likelihood of the function identified by MLE fitting the data. This seems really really really low.
What am I missing here?