Skip to main content
Tweeted twitter.com/StackStats/status/1047411520060248064
edited tags
Link
Carl
  • 13.3k
  • 7
  • 55
  • 115
Source Link
Carl
  • 13.3k
  • 7
  • 55
  • 115

Can one give an example(s) of when non-nested AIC model comparison is not useful for model selection?

Note: The question here is not the same as this one. Indeed, as an answer to that question the answer below was closed as unrelated, together with the suggestion (credit @gung) to ask a separate question.

Background: @JonesBC writes "Akaike himself thought that AIC was useful for comparing non-nested models." Moreover, @DavidJohnson writes "The derivation of AIC as an estimator of Kullback-Leibler information loss makes no assumptions of models being nested."

The basic assumption here is that non-nested models can be compared by AIC, and that is not really the case unless lots of other usually ignored conditions are met. It is not necessary to specify all of the conditions that should be met in order that AIC model selection be useful. It is sufficient to post a counter example, and that is the question here,

Question: What is non-nesting and what would a counterexample of not useful non-nested AIC comparison look like?