http://www.stat.wisc.edu/courses/st333-larget/aic.pdf
The AIC calculated with the model lm(SAT~1) was 560.4736, but the AIC calculated with stepwise selection starting with lm(SAT~1) was 419.42. May I ask why there is a difference? Thanks a lot.
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1$\begingroup$ Welcome to CV. Could you copy, or at least indicate the location of, the relevant part of the PDF? $\endgroup$– The LaconicNov 17, 2018 at 18:09
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$\begingroup$ the author demonstrated how to calculate AIC on page 2 and then demonstrated forward selection on the bottom of page 3 $\endgroup$– CeraVeUserNov 17, 2018 at 18:18
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$\begingroup$ These are two different models. The first has only an intercept, while the second has several variables as selected by forward selection. $\endgroup$– The LaconicNov 17, 2018 at 18:43
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$\begingroup$ > step(lm(SAT~1),SAT~.,direction="forward") Start: AIC=419.42 SAT ~ 1 Call: lm(formula = SAT ~ 1) Coefficients: (Intercept) 948.4 The starting AIC has considered several variables? $\endgroup$– CeraVeUserNov 17, 2018 at 18:49
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$\begingroup$ Ah. I misunderstood your question because I was confused about what you were looking at. $\endgroup$– The LaconicNov 17, 2018 at 21:12
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See the note in the referenced paper:
This is what the functions AIC and BIC calculate in R. The AIC and BIC formulas in your textbook ignore the leading two terms n + n log 2π and use p instead of p + 1.
It looks like the "step" function in R uses the latter convention. You'll find that the difference between the two AICs here is n + n log 2π + 2, which is a quantity that doesn't depend on the model itself, and so doesn't have any effect on model selection.
answered Nov 18, 2018 at 3:07