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# Re: st: Constrained regression question

 From Maarten Buis To statalist@hsphsun2.harvard.edu Subject Re: st: Constrained regression question Date Wed, 28 Mar 2012 09:43:38 +0200

```On Wed, Mar 28, 2012 at 12:04 AM, John Pfaff wrote:
> 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
>
> * I do not see any obvious way to impose restriction (2) when using invlogit.

This is how you impose restriction (2):
*---------------- begin example ------------------
sysuse auto, clear
generate mpg2 = -mpg
gen turn2 = turn*10
nl (mpg2 = invlogit({lgta})*price   +   ///
invlogit({lgtb})*turn2   +   ///
( 0.95 -                     ///
invlogit({lgta}) -           ///
invlogit({lgtb}) )*foreign + ///
{c})

nlcom  (price: invlogit(_b[lgta:_cons]))     ///
(turn2: invlogit(_b[lgtb:_cons]))     ///
(foreign: 0.95 -                      ///
invlogit(_b[lgta:_cons]) -  ///
invlogit(_b[lgtb:_cons]))
*----------------- end example -------------------
(For more on examples I sent to the Statalist see:
http://www.maartenbuis.nl/example_faq )

Hope this helps,
Maarten

--------------------------
Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen
Germany

http://www.maartenbuis.nl
--------------------------
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```