nls 系数的约束

Question

我正在尝试使用 nls() 函数拟合数据，其中数据的性质为我提供了一个系数和两个系数之和的界限。让我介绍一个简短的例子，看看问题出在哪里。我希望参数 b1 介于 0 和 1 之间，我希望参数 b1 和 b2 的总和也介于 0 和 1 之间。

set.seed(123)

# example where everything is OK
x <- 1:200
g <- rbinom(200, 1, 0.5)
y <- 3 + (0.7 + 0.2 * g) * x 
yeps <- y + rnorm(length(y), sd = 0.1)  

# both parameter b1 and sum of parameters b1 and b2 are between 0 and 1
nls(yeps ~ a + (b1 + b2 * g) * x, start = list(a = 0.12345, b1 = 0.54321, b2 = 0.4213))

# using more extreme values
x <- 1:200
g <- rbinom(200, 1, 0.5)
y <- 3 + (0.9 - 0.99 * g) * x 
yeps <- y + rnorm(length(y), sd = 15) 

# b1 is OK, but b1 + b2 < 0
nls(yeps ~ a + (b1 + b2 * g) * x, 
    start = list(a = 0.12345, b1 = 0.54321, b2 = 0.4213))

# trying constraints, not good, sum is still out of range
nls(yeps ~ a + (b1 + b2 * g) * x, 
    start = list(a = 0.12345, b1 = 0.54321, b2 = 0.4213),
    lower = list(a = -Inf, b1 = 0, b2 = -1),
    upper = list(a = Inf, b1 = 1, b2 = 1),
    algorithm = "port")

我正在寻找的是类似的东西（不起作用）：

nls(yeps ~ a + (b1 + b2 * g) * x, 
    start = list(a = 0.12345, b1 = 0.54321, b2 = 0.4213),
    lower = list(a = -Inf, b1 = 0, b2 = -b1),
    upper = list(a = Inf, b1 = 1, b2 = 1 - b1),
    algorithm = "port")

是否可以在nls()函数中设置其他参数的约束？感谢您的任何建议！

Answer 1

令 B2 = b1+b2 所以 b2 = B2-b1 并用 B2-b1 代替 b2 我们得到关于 a、b1 和 B2 的问题，其中后两者在 0 和 1 之间所以：

fm <- nls(yeps ~ a + (b1 + (B2-b1) * g) * x, lower = c(-Inf, 0, 0), upper = c(Inf, 1, 1),
    start = list(a = 0.1, b1 = 0.5, B2 = 0.1), alg = "port")

给出以下（因此 b2 = B2 - b1 = 0 - 0.9788 = -0.9788）

> fm
Nonlinear regression model
  model: yeps ~ a + (b1 + (B2 - b1) * g) * x
   data: parent.frame()
      a      b1      B2 
-5.3699  0.9788  0.0000 
 residual sum-of-squares: 42143

Algorithm "port", convergence message: both X-convergence and relative convergence (5)

和策划：

plot(yeps ~ x)
points(fitted(fm) ~ x, pch = 20, col = "red")

nls 系数的约束

Constraints for nls coefficients

r

nls