I note that some stepwise backwards elimination methods use AIC to make the decision about which variables to eliminate, and others use the F-statistic. Why would I use one over the other, and is there a justification for this choice? All the literature I’ve found just highlights that there are two approaches, and some say that “AIC is better than the F-statistics” but does not offer any explanation.

I am aware that stepwise regression is frowned upon in general, so hence this does not need to be a discussion on that aspect as there are a lot of posts on those aspects both here and in the research literature.

  • $\begingroup$ See Equivalence of AIC and p-values in model selection. I suspect any rigid preference for AIC - i.e. a p-value cut-off of 0.157 rather than the 0.05 you night be thinking of - comes from the asymptotic equivalence of selecting by AIC to selecting by leave-one-out cross validation, which seems relevant when the goal of the model selection is to improve predictive performance. Nevertheless, validation of the whole selection + fitting procedure often shows disappointing results & I'll link yet again to ... $\endgroup$ – Scortchi - Reinstate Monica Mar 23 '16 at 14:24
  • $\begingroup$ ... Algorithms for automatic model selection for the explanation (if not for your benefit, for that of other readers). $\endgroup$ – Scortchi - Reinstate Monica Mar 23 '16 at 14:25

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