Skip to content
Prev 16744 / 398498 Next
Original Raw

Hi,

Michael Roberts 
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)
On Tue, 29 Jan 2002, Michael Roberts wrote:

            

      
      
      
    

        
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.

[...]