regression

[riccardo85]

I have to run this linear regression

y = a +b1 x1 + b2 x2 +u

with b1, b2 >0  and b1+b2=1

proc reg would be perfect but it doesn't accept inequality constraints.

viceversa, proc nlin would be ok but it doesn't accept equality constraints.

one possibility would be proc nlin with

y= a + exp(c1) x1 + (1-exp(c1)) x2 + u

Do you have a better solution?

thank you

[PGStats]

In proc nlin, use bounds

bounds 0 < C < 1;

and equation

y = a + C x1 + (1-C) x2 + u;

[riccardo85]

thank you but with 3 (or more) parameters?

y=a0+ a1 x1 + a2 x2 + a3 x3

becomes

y= a0 + a1 x1 +a2 x2 + (1-a1-a2) x3

bounds 0< a1 < 1

bounds 0 < a2 <1

and the constraint  0 < a3 < 1 ?

[PGStats · Accepted solution]

bounds 0 < a1 < a2 < a3 < 1;
y = a0 + a1*x1 + (a2-a1)*x2 + (a3-a2)*x3 + (1-a3)*x4;

[Ksharp]

proc hpgenselect;
class A;
model y/n = A x / dist=binomial;
restrict A 1 0 -1;
restrict x 2 >= 0.5;
run;