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"?
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