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# Re: Rép. : Re: st: Inequality constraints in cnsreg

 From Steven Samuels <[email protected]> To [email protected] Subject Re: Rép. : Re: st: Inequality constraints in cnsreg Date Fri, 5 Nov 2010 17:59:02 -0400

```/*
```
Well, the second version was also incorrect. here's a version that _presumably_ is, but -nl-- doesn't converge (b1 - b2 is very close to zero). I thought that I had learned addition and subtraction at a younger age, but maybe not..
```

Steve
[email protected]

y =  b0 + b1 x1 + b2 x2 =
=  b0 + (b1 - b2) x1 +  + b2 (x2 +x1)

If b1 - b2 = exp(c)    where c = log(b1 - b2), then b1 - b2>0

Let z = x2 + x1

Then fit the *non-linear* equation

y = exp(c)*x1 + b2 Z
*/
***********CODE BEGINS******
sysuse auto, clear
keep if rep78 !=.
rename rep78 x1
rename  foreign x2
rename mpg y

gen z = x2 + x1
reg y x1 x2  //constraint not met

nl (y = {alpha} + exp({c})*x1 + {b2}*z)  //get constant & b2

nlcom b1: log(_b[c:_cons]) + _b[b2:_cons] // get b1
matrix b1x =r(b)

gen b1hat = el(b1x,1,1)

/* Get new prediction: no longer OLS */
gen yhatnew = _b[_cons] + b1hat* x1 + _b[b2:_cons]*x2

/* recompute Root MSE */

gen resid = y - yhatnew
gen resid2 = (y - yhatnew)^2
total resid2
local rmse = sqrt(r(b)/e(df_r))

di `rmse'   //compare to original Root MSE

*********CODE ENDS***********

---

I've just outlined a solution, Herve.  The rest is up to you.

Steve

Steven J. Samuels
[email protected]
18 Cantine's Island
Saugerties NY 12477
USA
Voice: 845-246-0774
Fax:    206-202-4783
On Nov 5, 2010, at 4:38 PM, Herve STOLOWY wrote:

Dear Steven:

I apologize because I have given first a simplified version of my model.
In other thread, I gave the full model.

Best regards

Hervé

```
```Steven Samuels  05/11/10 21:36 >>>
```
```---

--

Herve, I don't find the FAQ all that enlightening either.  Here is a
solution to a reduced problem:

y =  b0 + b1 x1 + b2 x2 =
= (b1 - b2) x1 +  + b2( x1 - x2)

If b1 - b2>0 then b1 - b2 = exp(c)  for some number c

Let z = x2 - x1

Then fit the *non-linear* equation

y = exp(c)*x1 + b2 Z
and solve for b2

***********CODE BEGINS******
sysuse auto, clear
keep if rep78 !=.
rename rep78 x1
rename  foreign x2
rename mpg y

gen z = x1 - x2
reg y x1 x2  //constraint not met

nl (y = {alpha} + exp({c})*x1 + {b2}*z)  //get constant & b2

nlcom b1: log(_b[c:_cons]) +_b[b2:_cons] // get b1
*********CODE ENDS***********

Steve

Steven J. Samuels
[email protected]
18 Cantine's Island
Saugerties NY 12477
USA
Voice: 845-246-0774
Fax:    206-202-4783

On Nov 5, 2010, at 2:07 PM, Herve STOLOWY wrote:

Dear Statalisters:

I am using Stata 11.1

I would like to use cnsreg to create the following constaints:

Y X1 X2 X3 X4
constriant 1 X2 > X1
constraint 2 X4 > X3

I have read the threads which existed a few years ago and a recent one
on the topic of inequality constraints
(http://www.stata.com/statalist/archive/2010-04/msg01437.html).

I have also read the answer from Marteen Buis and his suggested solution
(http://www.stata.com/support/faqs/stat/intconst.html).

I do not understand very well the suggested solution and I am not
trained in programming.

Consequently, my question is the following: is there a "not too complex"
solution to get the constraints I need?

Best regards

Hervé Stolowy

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```