R-beta: formula() and model formulae
Bill Venables
wvenable at attunga.stats.adelaide.edu.au
Wed May 7 10:54:03 CEST 1997
Peter Dalgaard writes:
> >
> > 2) if x is of mode numeric, then the model formula
> > mymod <- lm(y ~ x + x^2)
> > is not processed as S would do it. The model is fit[ted]
> > ignoring the x^2 term...
>
> We had that topic a while back. I think it was concluded that
> it is a feature, because mixing model formulas and arithmetic
> ditto is bad practice.
I don't recall we did, but in any case I'd like to re-open it.
There is an anomaly in the way : and ^ terms are handled in the
sense that the logical and useful thing is obvious but does not
happen. Let me give an example. Suppose a and b are factors, x
and y are not.
A term such as (a + b + x + y)^2 should be expanded out binomial
fashion, coefficients stripped away and the remaining products
treated as : products. Then S copes with terms like a:a, a:b and
a:x fine, even x:y is handled by having it generate a column of
xy-products, as it should.
But a term such as x:x does not generate a column of x-squares,
it is merely removed as it would be if it were a factor. This is
a complete anomaly, and one that I don't think would be hard or
dangerous for R to rectify. Indeed it would be very useful to
generate a complete second degree regression in three variables
using y ~ (1 + x1 + x2 + x3)^2. As it is now it generates linear
and product terms only and omits the powers. Go figure.
> (I don't have any strong feeling about this, personally. As
> long as R won't introduce those awful Helmert contrasts as
> default...)
Ah, the Helmert contrasts b\^ete noir. For ANOVA the contrast
matrix used is mostly irrelevant. For regression models I agree,
treatment contrasts would be generally more easily interpreted.
I presume the reason they were used at all is because if you have
equal replication of everything the Helmert contrasts give you a
model matrix with orthogonal columns, so all estimates are
uncorrelated. Whenever do you get equal replication, though?
--
Bill Venables, Head, Dept of Statistics, Tel.: +61 8 8303 5418
University of Adelaide, Fax.: +61 8 8303 3696
South AUSTRALIA. 5005. Email: Bill.Venables at adelaide.edu.au
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