[R] Marginal (type II) SS for powers of continuous variables in a linear model?

[Bjørn-Helge Mevik]

Prof Brian D Ripley <ripley at stats.ox.ac.uk> writes:

> On Tue, 12 Aug 2003, [iso-8859-1] Bjørn-Helge Mevik wrote:
>
>> Also, is this example (lm(y~x+I(x^2), Df)) really balanced?  I think
>
> No, and I did not use summary,aov on it!

And I didn't say you did!

>> This gives the SSs R(x | A, B, A:B, x^2), R(x^2 | A, B, A:B, x) and
>> R(A:B | A, B, x, x^2).  The SS for x is not marginal as defined
>> above.
>
> But that *is* how `marginal' is usually defined.

Ok.

> Why should I(x^2) be regarded as subservient to x?

In polynomial regression, it is usual to first consider a linear
model, then a quadratic, and so forth.  The interesting tests are usually
then the effect of a power of x whith all lower degree terms of x in the
model.  I thought it would be natural to treat polynomials of
continuous variables similarly in models with categorical variables as
well.

-- 
Bjørn-Helge Mevik