[R] OLS variables

[John Fox]

Dear Brian,

I don't have a strong opinion, but R's interpretation seems more consistent
to me, and as Kjetil points out, one can use polym() to specify a
full-polynomial model. It occurs to me that ^ and ** could be differentiated
in model formulae to provide both.

Regards,
 John

--------------------------------
John Fox
Department of Sociology
McMaster University
Hamilton, Ontario
Canada L8S 4M4
905-525-9140x23604
http://socserv.mcmaster.ca/jfox 
-------------------------------- 

> -----Original Message-----
> From: Prof Brian Ripley [mailto:ripley at stats.ox.ac.uk] 
> Sent: Monday, November 07, 2005 4:05 AM
> To: Kjetil Brinchmann halvorsen
> Cc: John Fox; r-help at stat.math.ethz.ch
> Subject: Re: [R] OLS variables
> 
> On Sun, 6 Nov 2005, Kjetil Brinchmann halvorsen wrote:
> 
> > John Fox wrote:
> >>
> >> I assume that you're using lm() to fit the model, and that 
> you don't 
> >> really want *all* of the interactions among 20 predictors: 
> You'd need 
> >> quite a lot of data to fit a model with 2^20 terms in it, 
> and might 
> >> have trouble interpreting the results.
> >>
> >> If you know which interactions you're looking for, then why not 
> >> specify them directly, as in lm(y ~  x1*x2 + x3*x4*x5 + 
> etc.)? On the 
> >> other hand, it you want to include all interactions, say, up to 
> >> three-way, and you've put the variables in a data frame, 
> then lm(y ~ .^3, data=DataFrame) will do it.
> >
> > This is nice with factors, but with continuous variables, 
> and need of 
> > a response-surface type, of model, will not do. For instance, with 
> > variables x, y, z in data frame dat
> >    lm( y ~ (x+z)^2, data=dat )
> > gives a model mwith the terms x, z and x*z, not the square terms.
> > There is a need for a semi-automatic way to get these, for 
> instance, 
> > use poly() or polym() as in:
> >
> > lm(y ~ polym(x,z,degree=2), data=dat)
> 
> This is an R-S difference (FAQ 3.3.2).  R's formula parser 
> always takes
> x^2 = x whereas the S one does so only for factors.  This 
> makes sense it you interpret `interaction' strictly as in 
> John's description - S chose to see an interaction of any two 
> continuous variables as multiplication (something which 
> puzzled me when I first encountered it, as it was not well 
> documented back in 1991).
> 
> I have often wondered if this difference was thought to be an 
> improvement, or if it just a different implementation of the 
> Rogers-Wilkinson syntax.
> Should we consider changing it?
> 
> -- 
> 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