I am trying to use the minpack.lm package to fit a non linear model to data with a constrain on the sum of two parameters. Here A_b+A_s<1, A_b>0, A_s>0 and k>0 are the constraints I want to optimize for, thus the log(A_b + A_s) and log(1 - (A_b + A_s)) functions.
I tried to reproduce the example given here.
However, the nlsLM throws an error, and I suspect it is because it is not able to put constraint on a sum of parameters, as opposed to a constraint to the value of a parameter only.
library(minpack.lm)
data <- data.frame(x = c(0.63, 0.67, 1.08, 1.37, 1.17, 1.34, 1.33, 1.48, 1.40, 1.58, 1.02, 1.48, 0.90, 0.55, 0.90), y = c(0.58, 0.61, 0.50, 0.51, 0.50, 0.47, 0.49, 0.51, 0.47, 0.48, 0.53, 0.43, 0.57, 0.68, 0.49))
n <- nrow(data)
mydata0 <- rbind(data, 0 * data[1:2,])
nlsLM(y ~ c(A_b + (A_s * k / x[1:n]) * log((x[1:n] + k) / k) ,
log(A_b + A_s),
log(1 - (A_b + A_s))),
mydata0,
start = list(A_b = 0.5, A_s = 0.5, k = 1))
