[R] Order of formula terms in model.matrix

peter dalgaard pdalgd at gmail.com
Mon Jan 18 00:39:21 CET 2016

> On 17 Jan 2016, at 19:34 , Charles C. Berry <ccberry at ucsd.edu> wrote:
> IIRC, there are some heuristics involved harking back to the White Book. I recall there have been discussions of whether and how this could be fixed before on this list and or R-devel, but I cannot seem to lay my browser on them right now.

And IIRC: yup, and one of the issues is that 
(a) some rules work left-to-right
(b) the logic is oblivious to the factor/vector distinction

For factors a,b,c, what happens for ~a:b + b:c is that a:b gets the full term expansion since the marginals a and b are not in the model but since b is part of the fully expanded a:b,  b:c gets the reduced form expansion as it would in ~b + b:c (the c-within-b thing). Swapping the terms gives you a different result, but at least it is the same model in the sense that the columns span the same subspace. 

If a and b are vectors, and c is a factor, you get the same logic: expand a:b fully, then treat b:c as in b + b:c. Unfortunately, a:b is just the product of a and b, whether or not it is fully expanded, so it doesn't really make sense to proceed as if b is contained in a preceding term. So the net result is that you end up with one column less than you probably wanted.

Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Office: A 4.23
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com

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