(Prediction) constrained OLS in R

Question

I have a collection of $n$ datapoints $(y_i,\bf{x}_i)$ in $\mathbb{R}^{p+1}$ and would like to estimate the following model in R:

$$\underset{\bf{b}\in\mathbb{R}^{p}}{\arg.\min}\;\sum_{i=1}^n(y_i-\bf{x}_i'\bf{b})^2$$

$$u.c.\;\;\;0\leq \bf{x}_i'\bf{b}\leq 1\;\;\;\forall i$$

anybody has a pointer to an efficient way of doing this? is there a re-parametrization of the OLS problem that would allow for this?

If you can tolerate a different link function, you could consider a logit- or probit- type model, perhaps. — Glen_b, Apr 25 '13 at 08:10
@Glen_b: thanks, but that's the thing: i'd like to use the linear link function. — user603, Apr 25 '13 at 09:02

score 1 · Accepted Answer · answered Apr 26 '13 at 21:50

It is a quadratic optimization problem, that can be solved with solve.QP (just expand the square to put it in the form expected by the function).

# Sample data
n <- 100
k <- 3
b <- c(-.1,.5,1)
x <- matrix( runif(n*k), nc=k )
y <- x %*% b + .1*rnorm(n)

# Solve the quadratic program
library(quadprog)
r <- solve.QP(
  t(x) %*% x,
  t(y) %*% x,
  t(rbind( x, -x )),
  c(rep(0,n), rep(-1,n))
)
r$solution

# Check that the constraints are satisfied
range( x %*% r$solution )  # in [0,1]
range( x %*% b          )  # wider

cool! thanks (also the internet is small world, thanks for your R guides)... — user603, Apr 26 '13 at 22:01

(Prediction) constrained OLS in R

1 Answers1