AIC values (from a fitted model, for example) are positive. So are the likelihood values. Are the log-likelihood values positive or negative? Here, in Wikipedia page concerning likelihood ratio test the log-likelihood values are negative and the less negative value indicates better fit.
But in this page, there is -(log-likelihood) (meaning negative of the log-likelihood) and it says that more negative value indicates better fit. In R the logLik-function from a model gives negative values, but if I have only the likelihood and I want a log-likelihood from it, I have to take negative of the logarithm???
So my question is fairly simple, when comparing those values (AIC, likelihood, logarithmic likelihood) from 2 different models, which (of which kind, more or less negative) value indicates better model?
Here is also some statistic as an example, could some one "translate" this info as words for me =) (I am using msts and tbats from forecast-function)
> fit1$likelihood  90871.47 > fit2$likelihood  90785.92 > fit1$AIC  90909.47 > fit2$AIC  90839.92 # AIC from likelihood, par1 refers to number of fitted parameters > 2*par1-2*log(fit1$likelihood)  -14.8344 > 2*par2-2*log(fit2$likelihood) # AIC from likelihood  -10.83252
So why I wont get the same AIC values when calculating "by hand"? Which one are the correct ones?