[R] Almost a GAM?

[Michael Roberts]

>>> Simon Wood <snw at mcs.st-and.ac.uk> 01/30/02 04:28AM >>>
> Wouldn't an "interaction"
> between a smooth function f(x,y) and a continuous covariate w be
another
> smooth function g(x,y,w), say? But in this case:
> y~g(x,y,w1)+f(x,y,w2)+e 
> won't generally be identifiable, without imposing extra structure on
the
> model [for example g1(x,y)+g2(w1) is a valid g(x,y,w1), while 
> f1(x,y)+f2(w2) is a valid f(x,y,w2) - clearly there's an
identifiability
> problem with f1 and g1!]. 
- Sorry, this was wrong (Chong Gu is right). The model is identifiable
subject only to side conditions on the basis of completely smooth
components of f and g - identifiability of the non-smooth components
seems
to come about because the solution of the smoothing problem involving
f(x,y,w) simply cannot have the form f1(x,y)+f2(w). Unfortunately mgcv
doesn't impose the necessary side conditions, so you can't use it to
estimate
y~g(x,y,w1)+f(x,y,w2)+e
[...yet]  
cheers,
Simon

....
Sorry to drag this out further.

This has been a great help. Although I thought that ssanova in gss 
would solve my problem, now I do not think so.

I do not want to estimate
y~g(x,y,w1) + f(x,y,w2) + e

This would be too expensive besides.

I would like to estimate
y~g(x,y)*w1 + f(x,y)*w2 + e without any of the expansion terms.

w1 and w2 are continuous. 

I don't see how to specify such a functional form in ssanova

This is much more restrictive than the form above and
cheap enough to do on my computer (I think).  It is also
makes good sense for my problem.

Right now I see four potential routes:

1) try to augment Simon's mgcv (rework the design matrix)

2) try to augment Chong Gu's (at this point I have no idea if this is
doable)

3) try backfitting the smooth terms in conjunction with ssanova or
another
smooth regression technique.

4) try a "crude" approximation by descretizing w1 and w2 into factor
levels
and use the technique first suggested by Vito.

Any suggestions on the most promissing route would be 
greatly appreciated. (one of these or something else?)

Many thanks,

Michael



Michael J. Roberts

Resource Economics Division
Production, Management, and Technology
USDA-ERS
(202) 694-5557 (phone)
(202) 694-5775 (fax)
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