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.