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Re: st: re: constraints

From   "Vidya Mahambare" <[email protected]>
To   <[email protected]>
Subject   Re: st: re: constraints
Date   Wed, 29 Jun 2005 07:39:46 +0100

Following Kit's suggestion I redefined the constraint   L.wpi+L2.wpi+L3.wpi=1 as
b(L3) = 1-b(L)-b(L2), and regressed 
(wpi - L.wpi)  on (L.wpi-L3.wpi), (L2.wpi-L3.wpi) and other variables.

This does not produce a correct R^2, as Richard suspected. It is much lower
because of variables transformations, I think. Is there a way to to calculate a
correct R^2 after using -reg- for this problem?


>>> [email protected] 06/29/05 5:20 AM >>>
At 06:45 PM 6/28/2005 -0400, Kit Baum wrote:
>Although cnsreg is useful, it is hardly necessary for Vidya's problem:
>"I am trying to estimate an equation similar to this -
>constraint define 1 L.wpi+L2.wpi+L3.wpi=1
>cnsreg wpi L.wpi L2.wpi L3.wpi L.ygapm L2.ygapm sswpi L.sswpi, constraint(1)"
>This constraint may be rewritten as b(L3) = 1-b(L)-b(L2)  and merely 
>substituted into the equation,
>(wpi - L.wpi)   regressed on (L.wpi-L3.wpi),  (L2.wpi-L3.wpi) and the rest
>which you can estimate with regress, robust.
>If you want the coefficient on L3.wpi, calculate it via lincom.

Since I made the claim that many/most/all problems involving (linear) 
constraints could be handled by regular regression as well as by cnsreg, I 
am glad Kit was able to do the algebra on this one!  However, does this 
produce a correct R^2, which is what Vidya was seeking in the first 
place?  I was thinking of situations where all the manipulations could be 
done on the RHS, but here the LHS has to be changed.

Richard Williams, Notre Dame Dept of Sociology
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