[R] Hi,

[Chong Gu]

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   Date: Tue, 29 Jan 2002 21:18:40 -0500
   From: "Michael Roberts" <mroberts at ers.usda.gov>
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   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)


gss would in principal fit y~x*y*w1+x*z*w2 for you, but the current
algorithm is too slow for the sample size needed for fitting such a
model successfully.

As for identifiability, the current form MIGHT be okey, but are you
sure y=e for w1=w2=0?

Chong Gu
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