Exploring aic (Akaike Information Criterion)

Goodness of Fit of Statistical Models 

aic plays a key role in the interpretation of efficiency of probability models with respect to a model of reference. Here the ratio of two likelihood functions is taken and it is equivalent to the difference between the two loglikelihood functions. So the greater the difference between loglikelihood functions the greater is the difference in efficiency  between the models.

aic=-log(L(P1)/L(P2))+k

Here P1 is estimator of the parameter of model 1 and L(P1) is the likelihood function obtained from probability model 1. L(P2) is the likelihood function obtained from probabilitymodel 2, with P2 as the estimator of the parameter of this model. k is the degree of freedom.

aic = -[log(L(P1))-log(L(P2))]+k

This expression shows that the greater the difference [log(L(P1))-log(L(P2))] the higher the value of aic. So high value of difference indicates greater dissimilarity between model 1 and model 2. For relatively close models aic should be lower than the aic of relatively distant models. Smaller value of aic implies that the fit is good. The model with higher value of aic ( with respect to a model of reference)should be rejected.