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Can AIC compare nested models?
The AIC does not require nested models. One of the neat things about the AIC is that you can compare very different models. However, make sure the likelihoods are computed on the same data. Beware of AIC values computed using conditional likelihoods because the conditioning may be different for different models.
How do you know if a model is nested?
Two models are nested if one model contains all the terms of the other, and at least one additional term. The larger model is the complete (or full) model, and the smaller is the reduced (or restricted) model.
Can you compare AIC of two non nested models?
The penalty term in the expression for AIC is what allows this comparison. But no assumptions are made about the functional form of the asymptotic distribution of the differences between the AIC of two non-nested models when doing the model comparison, and the difference between two AICs is not treated as a test statistic.
Which is better BIC or AIC for model selection?
Compared to the BIC method (below), the AIC statistic penalizes complex models less, meaning that it may put more emphasis on model performance on the training dataset, and, in turn, select more complex models. We see that the penalty for AIC is less than for BIC.
How does the derivation of Bic relate to AIC?
Importantly, the derivation of BIC under the Bayesian probability framework means that if a selection of candidate models includes a true model for the dataset, then the probability that BIC will select the true model increases with the size of the training dataset. This cannot be said for the AIC score.
When to use AIC or chi-squared test?
“If two models are nested (i.e. one is a sub-set of the other) then the more usual chi-squared test is the most appropriate to use. If the models are not nested, the AIC can be used…” Can anyone elaborate on this and/or explain why AIC is not as helpful as likelihood ratio tests on nested models?