Hi,
Sorry for the confusion.
I would like to estimate a model wherein
the marginals of z with respect to w1 and w2
are smooth functions of x and y. I have data
on z, x, y, w1 and w2.
so E[dz/dw1] = f(x,y) and E[dz/dw2] = g(x,y)
and I would like to estimate f(x,y) and g(x,y)
I suppose I could try to fit something more general
using projection pursuit, but the nature of the problem
suggests the above structure.
For some reason I thought
x:y:z
would fit just the interaction term
xyz
and not expend to
x + y + z + xy +xz + yz + xyz
like x*y*z, which is why I wrote it the way I did.
So maybe it should have bern written
y ~ I(f(x,y)*w1) + I(g(x,y)*w2) + e
e is a symmetric random error.
This seems identifiable to me, but am I missing something?
Michael J. Roberts
Resource Economics Division
Production, Management, and Technology
USDA-ERS
(202) 694-5557 (phone)
(202) 694-5775 (fax)
>>> Prof Brian D Ripley <ripley at stats.ox.ac.uk> 01/29/02
12:30PM >>>
On Tue, 29 Jan 2002, Michael Roberts wrote:
> I don't think I can solve my problem in this way because w1
> and w2 are continuous variables.
>
> A second problem is that my f(x,y) is not f(x, df), i.e., I'd
> like to have a sum of *two* dimensional smoothers interacted
> with other variables.
>
> After my first post I did find a discussion of this problem on the
> S archive, which suggested the same appraoch as Vito did. S can
> fit 2-d smooths, but still can't handle the interaction terms.
I think you need to define carefully what you mean. I had no idea what
z ~ f(x,y):w1 + g(x,y):w2 + e
is about, and now you tell me w1 and w2 are continuous I have even
less
idea. What is the interaction you are talking about? And how can the
model possibly be identifiable?
`:' is S model notation for an interaction, and at least one of the
components is a factor (otherwise special rules apply, generally
multiplication). But smooth functions cannot be factors.
[...]
--
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 272860 (secr)
Oxford OX1 3TG, UK Fax: +44 1865 272595
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