[R] All possible subset selection?

[Prof Brian Ripley]

On Wed, 7 May 2003, zhu wang wrote:

> I am wondering if there is a function in R to do all
> possible subset selection, e.g. using AIC/BIC. It
> seems to me the function step can not do all possible
> selection.

That's right, and I know of no function.  Potentially the computational 
burden is horrendous, even of sorting out which are valid subset models.
For continuous (rather than categorical) variables, look at package leaps.

> I am also want to know why the following functions
> give me different results. It seems I missed some
> points here.
> 
> lm <- lm(y ~., data=somedata)
> AIC(lm)
> extractAIC(lm)

Please don't call the result by the name of a function!

extractAIC (as its help says) is a helper function for step/add1/drop1,
and it is designed to report Cp in some lm cases when AIC is Cp plus a
constant. It predates AIC by several years.

Remember that AIC is only defined up to an additive constant, because a 
log-likelihood is (it depends on the dominating measure used).  
extractAIC.lm and AIC.lm use different ones, and in the case that the 
scale is known, they use different maximizations too.  (AIC.lm is only 
appropriate if the scale (error variance) is unknown.)

-- 
Brian D. Ripley,                  ripley at 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 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595