After some correspondence with Jim Robison-Cox I now understand
what he meant (but did not say). When you run step.lm with trace=T,
you get intermediate printout from drop1.lm and/or add1.lm. That
is labelled Cp (but is not output from step() itself), whereas
the output from step.lm is labelled AIC.
Reason: they are not the same thing! step.lm is a call to step.glm,
and for a non-gaussian(identity) GLM the `Cp' is based on a linearization
at that step and not at all comparable in general with the `AIC'.
It does not help that `Cp' is not C_p as defined by Mallows, nor C_p
as defined by most other references I consulted (RSS/sigma^2 + 2p, with
no -n) nor is `AIC' AIC as defined by Akaike, nor that the quote from the
S-PLUS 3.x manual is highly misleading nor that Dr Robison-Cox has
not noticed that the output shown in V&R MASS2 p 220-2 is actually from
step().
The biggest diffulty is perhaps that `AIC and Cp are equivalent measures'
only if sigma^2 is assumed known, and it is not in the software.
By the way, using Mallows' C_p approximately p only makes sense to me
if sigma^2 is known: it is then equivalent to s^2 \approx sigma^2
which is probably easier to use.
stepAIC was originally written to overcome problems with stepwise
fitting of GLMs, but does do a consistent job for linear models
with unknown sigma^2. Do note that even lm and its ancilliaries
do not do a consistent job if sigma^2 is known.
-- Brian D. Ripley, ripley@stats.ox.ac.uk Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/ University of Oxford, Tel: +44 1865 272861 (self) 1 South Parks Road, +44 1865 272860 (secr) Oxford OX1 3TG, UK Fax: +44 1865 272595 ----------------------------------------------------------------------- This message was distributed by s-news@wubios.wustl.edu. To unsubscribe send e-mail to s-news-request@wubios.wustl.edu with the BODY of the message: unsubscribe s-news