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Re: st: Constrained regression question


From   Jorge Eduardo Pérez Pérez <perez.jorge@ur.edu.co>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   Re: st: Constrained regression question
Date   Tue, 27 Mar 2012 23:51:58 -0400

You can modify example 6 of the FAQ you posted to restrict your
coefficients to add up to 0.95 and to be between 0 and 1. Simply
define the last coefficient as 0.95 times the coefficient, i.e, with
three coefficients:

a2 = 0.95*exp(t2)/(1+exp(t2)+exp(t3))
a3 = 0.95*exp(t3)/(1+exp(t2)+exp(t3))
a1 = 0.95/(1+exp(t2)+exp(t3))

_______________________
Jorge Eduardo Pérez Pérez



On Tue, Mar 27, 2012 at 6:04 PM, John Pfaff <JPFAFF@law.fordham.edu> wrote:
> Hello,
>
> I am curious if it is possible to use Stata to estimate a set of weights. My basic problem is the following:
>
> I have data on R_t for years t = 1988 to 2008
> I have data on A_t for years t = 1977 to 2008
>
> I want to see how well I can approximate R_t using 11 lagged years of A_t. In other words, I want to estimate the weights w_s in the following equation:
>
> R_t = w0*A_t + w1*A_(t-1) + w2*A_(t-2) + ... + w11*A_(t-11)
>
> The catch is that I have two sets of restrictions:
>
> (1) For each w_s, 0 < w_s < 1.
> (2) Also, w0 + w1 + ... + w11 = 0.95
>
> Simply running a simple regression fails, since restriction (1) is violated numerous times (lots of negative weights).
>
> I started at http://www.stata.com/support/faqs/stat/interval-constraints.html, which showed me how to satisfy restriction (1). But two problems arise:
>
> * The non-linear regression dropped 7 of the 11 A variables.
> * I do not see any obvious way to impose restriction (2) when using invlogit.
>
> Is there a better way to accomplish this? Thank you for any assistance!
>
> John
>
>
> *
> *   For searches and help try:
> *   http://www.stata.com/help.cgi?search
> *   http://www.stata.com/support/statalist/faq
> *   http://www.ats.ucla.edu/stat/stata/
>
>


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