[R] Constraint Linear regression

[R. Michael Weylandt]

Due to perfect collinearity, your regression isn't unique so you're
not going to be able to even solve the unconstrained version of this
problem.

Michael

On Tue, Mar 20, 2012 at 12:54 AM, priya fernandes
<priyyafernandes at gmail.com> wrote:
> Hi there,
>
> I am trying to use linear regression to solve the following equation -
>
> y <- c(0.2525, 0.3448, 0.2358, 0.3696, 0.2708, 0.1667, 0.2941, 0.2333,
> 0.1500, 0.3077, 0.3462, 0.1667, 0.2500, 0.3214, 0.1364)
> x2 <- c(0.368, 0.537, 0.379, 0.472, 0.401, 0.361, 0.644, 0.444, 0.440,
> 0.676, 0.679, 0.622, 0.450, 0.379, 0.620)
> x1 <- 1-x2
>
> # equation
> lmFit <- lm(y ~ x1 + x2)
>
> lmFit
> Call:
> lm(formula = y ~ x1 + x2)
>
> Coefficients:
> (Intercept)           x1           x2
>    0.30521     -0.09726           NA
>
> I would like to *constraint the coefficients of x1 and x2 to be between 0,1*.
> Is there a way of adding constraints to lm?
>
> I looked through the old help files and found a solution by Emmanuel using
> least squares. The method (with modification) is as follows -
>
>  Data1<- data.frame(y=y,x1=x1, x2=x2)
>
> # The objective function : least squares.
>
> e<-expression((y-(c1+c2*x1+c3*x2))^2)
>
> foo<-deriv(e, name=c("c1","c2","c3"))
>
> # Objective
>
> objfun<-function(coefs, data) {
>
> return(sum(eval(foo,env=c(as.list(coefs), as.list(data)))))
>
> }
>
> # Objective's gradient
>
> objgrad<-function(coefs, data) {
>
> return(apply(attr(eval(foo,env=c(as.list(coefs), as.list(data))),
>
>  "gradient"),2,sum))
>
>  }
>
> D1.unbound<-optim(par=c(c1=0.5, c2=0.5, c3=0.5),
>
>  fn=objfun,
>
> gr=objgrad,
>
> data=Data1,
>
>  method="L-BFGS-B",
>
>  lower=rep(0, 3),
>
> upper=rep(1, 3))
>
>
> D1.unbound
>
>
> $par
>         c1          c2          c3
> 0.004387706 0.203562156 0.300825550
>
> $value
> [1] 0.07811152
>
> $counts
> function gradient
>       8        8
>
> $convergence
> [1] 0
>
> $message
> [1] "CONVERGENCE: REL_REDUCTION_OF_F <= FACTR*EPSMCH"
>
> Any suggestion on how to fix the error  "CONVERGENCE: REL_REDUCTION_OF_F <=
> FACTR*EPSMCH"?
>
>        [[alternative HTML version deleted]]
>
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