Hello everybody.
I would have two quick theoretical questions on the AIC, which raised when performing some regression analysis in Stata.
Firstly, when comparing two nested models, the best fit can be expressed by the AIC: 2k - 2ln(L).
Now, I have two models;
Model 1 with: AIC = 301, ln(L) = - 470, Pseudo R^2 = 0.12
Model 2 with: AIC = 1200, ln(L) = - 560, Pseudo R^2 = 0.07
The question is: is it correct to affirm that Model 1 is to be preferred over Model 2, since the former has a larger Pseudo R^2 and a lower AIC, AND, at the same time, a lower ln(L) (the log-likelihood)? Does that mean, also, that when the log-likelihood is negative, I should select the model with the higher (ie closer to 0) ln(L)?
Secondly, I wanted to ask whether it is possible to use the AIC to compare the same model but estimated through two different estimators (GMM and ML, eg), or if in this case, using the AIC is usueless and I should consider just the log-likelihood.
Thanks!
Kodi
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