Here is a demonstration of how to solve your problem :
n <- 30 # You might need more than 6 data points to get good estimates for 3 parameters x1 <- rnorm(n) x2 <- runif(n) x3 <- rbinom(n, size=1, prob=0.4) A <- cbind(x1, x2, x3) # 30 x 3 matrix of independent variables b <- c(-1, 0.5, 0.2) # Note: the last component is out of bounds! y <- A %*% b + rnorm(n, sd=0.1) qr.solve(A, y) # unconstrained LS solution # Implementing the bounds (there is probably a better way to do this) # nc <- ncol(A) c1 <- matrix(0, nc, nc) diag(c1) <- 1 c2 <- matrix(0, nc, nc) diag(c2) <- -1 cmat <- rbind(c1, c2) Cmat <- cmat[c(2,5,3,6), ] # Constraint matrix G b0 <- c(0, -1, -1, 0) require(limSolve) ans <- lsei(A = A, B = y, G = Cmat, H = b0) ans While ans$X gives you the point estimates, it is a bit tricky to get standard errors. Hope this helps, Ravi. ---------------------------------------------------------------------------- ------- Ravi Varadhan, Ph.D. Assistant Professor, The Center on Aging and Health Division of Geriatric Medicine and Gerontology Johns Hopkins University Ph: (410) 502-2619 Fax: (410) 614-9625 Email: rvarad...@jhmi.edu Webpage: http://www.jhsph.edu/agingandhealth/People/Faculty_personal_pages/Varadhan.h tml ---------------------------------------------------------------------------- -------- -----Original Message----- From: r-help-boun...@r-project.org [mailto:r-help-boun...@r-project.org] On Behalf Of Stu @ AGS Sent: Tuesday, May 26, 2009 2:12 PM To: r-help@r-project.org Subject: [R] Linear Regression with Constraints Hi! I am a bit new to R. I am looking for the right function to use for a multiple regression problem of the form: y = c1 + x1 + (c2 * x2) - (c3 * x3) Where c1, c2, and c3 are the desired regression coefficients that are subject to the following constraints: 0.0 < c2 < 1.0, and 0.0 < c3 < 1.0 y, x1, x2, and x3 are observed data. I have a total of 6 rows of data in a data set. Is "optim" in the stats package the right function to use? Also, I can't quite figure out how to specify the constraints. Thank you! -Stu ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
