Linear Regressions with constraint coefficients
This is a quadratic programming problem that you can solve using either a quadratic programming solver with constraints or a general nonlinear solver with constraints. See https://cran.r-project.org/web/views/Optimization.html for more info on what is available. Here is an example using a nonlinear least squares solver and non-negative bound constraints. The constraint that the coefficients sum to 1 is implied by dividing them by their sum and then dividing the coefficients found by their sum at the end: # test data set.seed(123) n <- 1000 X1 <- rnorm(n) X2 <- rnorm(n) X3 <- rnorm(n) Y <- .2 * X1 + .3 * X2 + .5 * X3 + rnorm(n) # fit library(nlmrt) fm <- nlxb(Y ~ (b1 * X1 + b2 * X2 + b3 * X3)/(b1 + b2 + b3), data = list(Y = Y, X1 = X1, X2 = X2, X3 = X3), lower = numeric(3), start = list(b1 = 1, b2 = 2, b3 = 3)) giving the following non-negative coefficients which sum to 1 that are reasonably close to the true values of 0.2, 0.3 and 0.5:
fm$coefficients / sum(fm$coefficients)
b1 b2 b3 0.18463 0.27887 0.53650 On Tue, Apr 26, 2016 at 8:39 AM, Aleksandrovic, Aljosa (Pfaeffikon)
<Aljosa.Aleksandrovic at man.com> wrote:
Hi all, I hope you are doing well? I?m currently using the lm() function from the package stats to fit linear multifactor regressions. Unfortunately, I didn?t yet find a way to fit linear multifactor regressions with constraint coefficients? I would like the slope coefficients to be all inside an interval, let?s say, between 0 and 1. Further, if possible, the slope coefficients should add up to 1. Is there an elegant and not too complicated way to do such a constraint regression estimation in R? I would very much appreciate if you could help me with my issue? Thanks a lot in advance and kind regards, Aljosa Aleksandrovic Aljosa Aleksandrovic, FRM, CAIA Quantitative Analyst - Convertibles aljosa.aleksandrovic at man.com Tel +41 55 417 7603 Man Investments (CH) AG Huobstrasse 3 | 8808 Pf?ffikon SZ | Switzerland -----Original Message----- From: Kevin E. Thorpe [mailto:kevin.thorpe at utoronto.ca] Sent: Dienstag, 26. April 2016 14:35 To: Aleksandrovic, Aljosa (Pfaeffikon) Subject: Re: Linear Regressions with constraint coefficients You need to send it to r-help at r-project.org however. Kevin On 04/26/2016 08:32 AM, Aleksandrovic, Aljosa (Pfaeffikon) wrote:
Ok, will do! Thx a lot! Please find below my request: Hi all, I hope you are doing well? I?m currently using the lm() function from the package stats to fit linear multifactor regressions. Unfortunately, I didn?t yet find a way to fit linear multifactor regressions with constraint coefficients? I would like the slope coefficients to be all inside an interval, let?s say, between 0 and 1. Further, if possible, the slope coefficients should add up to 1. Is there an elegant and not too complicated way to do such a constraint regression estimation in R? I would very much appreciate if you could help me with my issue? Thanks a lot in advance and kind regards, Aljosa Aleksandrovic Aljosa Aleksandrovic, FRM, CAIA Quantitative Analyst - Convertibles aljosa.aleksandrovic at man.com Tel +41 55 417 7603 Man Investments (CH) AG Huobstrasse 3 | 8808 Pf?ffikon SZ | Switzerland -----Original Message----- From: Kevin E. Thorpe [mailto:kevin.thorpe at utoronto.ca] Sent: Dienstag, 26. April 2016 14:28 To: Aleksandrovic, Aljosa (Pfaeffikon); r-help-owner at r-project.org Subject: Re: Linear Regressions with constraint coefficients I believe I approved a message with such a subject. Perhaps there was another layer that subsequently rejected it after that. I didn't notice any unusual content. Try again, making sure you send the message in plain text only. Kevin On 04/26/2016 08:16 AM, Aleksandrovic, Aljosa (Pfaeffikon) wrote:
Do you know where I get help for my issue? Thanks in advance and kind regards, Aljosa Aljosa Aleksandrovic, FRM, CAIA Quantitative Analyst - Convertibles aljosa.aleksandrovic at man.com Tel +41 55 417 7603 Man Investments (CH) AG Huobstrasse 3 | 8808 Pf?ffikon SZ | Switzerland -----Original Message----- From: R-help [mailto:r-help-bounces at r-project.org] On Behalf Of r-help-owner at r-project.org Sent: Dienstag, 26. April 2016 14:10 To: Aleksandrovic, Aljosa (Pfaeffikon) Subject: Linear Regressions with constraint coefficients The message's content type was not explicitly allowed
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