topic Re: OLS with parameter restriction in SAS Programming

OLS with parameter restriction

jkim197 — Thu, 03 Sep 2020 15:19:32 GMT

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

Re: OLS with parameter restriction

PaigeMiller — Thu, 03 Sep 2020 15:29:06 GMT

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-coefficients/m-p/473076 (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.

Re: OLS with parameter restriction

jkim197 — Thu, 03 Sep 2020 15:44:59 GMT

Thanks but I didnt mean to do Bayesian inference

Re: OLS with parameter restriction

PaigeMiller — Thu, 03 Sep 2020 15:57:03 GMT

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

Remember, Google is your friend in situations like this.

Re: OLS with parameter restriction

PGStats — Thu, 03 Sep 2020 17:07:48 GMT

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

Re: OLS with parameter restriction

Ksharp — Fri, 04 Sep 2020 12:42:22 GMT

Check @Rick_SAS blog ,about this question.

Re: OLS with parameter restriction

jkim197 — Fri, 04 Sep 2020 13:04:53 GMT

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;

Re: OLS with parameter restriction

Rick_SAS — Sun, 04 Oct 2020 10:30:11 GMT

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