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

Bill Venables (
Fri, 27 Feb 1998 11:27:17 +1030

Jim Robison-Cox writes:
> ...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?

This has long been a puzzle for me, too, especially when you
realise that the original S developers (not S-PLUS) and Colin
Mallows work in the same building in Murray Hill. It's an
enigma. You know what my suggestion will be: use Brian's much
slicker, tidier and more general stepAIC.

Bill Venables.

Bill Venables, Head, Dept of Statistics,    Tel.: +61 8 8303 5418
University of Adelaide,                     Fax.: +61 8 8303 3696
South AUSTRALIA.     5005.   Email:

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