OLS with parameter restriction

[jkim197]

Hello sas users

Can anyone help me estimate OLS with restriction?

My model is

Y=b0+b1*x1+b2*x2+b3*x3

I want to impose restrictions where

(i) b1,b2,b3>=0 

(ii) b1+b2+b3=1

Which procedure do I use?

If you let me know it will be really appreciated

[PaigeMiller]

PROC REG with the RESTRICT statement can handle your second restriction, but not the first (because PROC REG cannot handle greater than or less than restrictions).

Then there's this: https://communities.sas.com/t5/Statistical-Procedures/Regression-analysis-with-only-positive-coeffic... (scroll down to the reply by @stanmarciano 

I believe you can program PROC IML to handle greater than or less than restrictions on the regression coefficients, but I leave that up to our in-house PROC IML author @Rick_SAS. 

[jkim197]

Thanks but I didnt mean to do Bayesian inference

[PaigeMiller]

And this: https://support.sas.com/kb/22/800.html

Remember, Google is your friend in situations like this.

[PGStats]

Replace b3 with 1 - b1 - b2 in your model and use proc nlin to fit your model with a bounds statement.

[Ksharp]

Check @Rick_SAS  blog ,about this question.

[jkim197 · Accepted solution]

proc model data=loading_&howmany(where=(year(date)=&i)) plots=none;
by wficn date;
retmrf=b0+b1*rm+b2*smb+b3*hml+b4*umd ;
bounds 0 <= b1 b2 b3 b4;
restrict b1+b2+b3+b4 = 1;
fit retmrf ;
ods output ResidSummary=rsq_&howmany._&i(keep=wficn date RSquare);
run;
quit;

[Rick_SAS]

For more about solving regression problems in SAS that have constraints on the parameters, see

• Restricted least squares regression in SAS  (equality constraints only)
• Regression with inequality constraints on parameters