# [R] Constrained OLS regression

Dimitris Rizopoulos dimitris.rizopoulos at med.kuleuven.be
Wed Sep 27 13:22:02 CEST 2006

```you could reparameterize, e.g.,

x1 <- runif(100, -4, 4)
x2 <- runif(100, -4, 4)
X <- cbind(1, x1 , x2)
y <-  rnorm(100, as.vector(X %*% c(5, -3, 4)), 2)
######################

fn <- function(betas){
betas <- c(betas, 1 - betas[2])
crossprod(y - X %*% betas)[1, ]
}

opt <- optim(c(5, -3), fn, method = "BFGS")
c(opt\$par, 1 - opt\$par[2])

I hope it helps.

Best,
Dimitris

----
Dimitris Rizopoulos
Ph.D. Student
Biostatistical Centre
School of Public Health
Catholic University of Leuven

Tel: +32/(0)16/336899
Fax: +32/(0)16/337015
Web: http://med.kuleuven.be/biostat/
http://www.student.kuleuven.be/~m0390867/dimitris.htm

----- Original Message -----
From: "Mesomeris, Spyros [CIR]" <spyros.mesomeris at citigroup.com>
To: <r-help at stat.math.ethz.ch>
Sent: Wednesday, September 27, 2006 12:51 PM
Subject: [R] Constrained OLS regression

> Hello R helpers,
>
> I am trying to do a linear OLS regression of y on two variables x1
> and
> x2. I want to constrain the coefficients of x1 and x2 to sum up to
> 1.
> and therefore run a constrained OLS. Can anybody help with this? (I
> have
> seen some answers to similar questions but it was not clear to me
> what I
> need to do) - I have tried the lm function with offset but I must
> not
> have used it properly.
>
> Thanks,
> Spyros
>
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