[S] Why is AIC labeled Cp in step()?

Jim Robison-Cox (jimrc@mathfs.math.montana.edu)
Thu, 26 Feb 1998 11:44:42 -0700 (MST)

Hello all,

I'm teaching a linear models course to stat grad students. Since I
know they will eventually run into people who use stepwise methods of
model selection, I'm trying to explain how those methods work. (All the
better to express my deep distrust of their black-box-iness) I realize
that in normal theory linear models AIC and Cp are equivalent measures,
but I don't understand why the step(), add1() and drop1() functions give
a column labeled Cp which is really AIC.

Quoting from the _Guide to Stat & Math Analysis_ p 7-13:

" The Cp statistic (actually what is shown is the AIC statistic, the
likelihood version of the Cp statistic - the two are related by the
equation AIC=sigmahat^2(Cp+n)) provides a convenient criterion for
determining whether a model is improved by dropping a term."

I also see in V&R MASS2 p 220-2 that their stepAIC() does actually print
AIC at the top of the column.

My concern is that people see the column labeled Cp and think that a
good model will have values close to p (# of parameters). Is there some
reason that this column has been mislabeled? Could we get it changed?

Jim Robison-Cox ____________
Department of Math Sciences | | phone: (406)994-5340
2-214 Wilson Hall \ BZN, MT | FAX: (406)994-1789
Montana State University | *_______|
Bozeman, MT 59717 \_| e-mail: jimrc@math.montana.edu

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