nls() : "Error in nlsModel(formula, mf, start, wts) : singular gradient matrix at initial parameter estimates "

Question

我正在尝试使用 nls()，但我一直收到错误

Error in nlsModel(formula, mf, start, wts) : singular gradient matrix at initial parameter estimates

我不确定问题出在哪里。

代码如下：

TI <- c(0.5, 2, 5, 10, 30)
prices <- cbind(zi, TI)
prices = as.data.frame(prices)

lnz_i <- function(TI, Alpha, Beta, Sigma) -TI*(Alpha*(1 - exp(-Beta*TI)) / (Beta) - (Sigma^2/2)*(1 - exp(-Beta*TI)) / (Beta)^2) - 0.02*(1 - exp(-Beta*TI)) / (Beta)

nls(zi ~ lnz_i(TI, Alpha, Beta, Sigma), start = c(Alpha = 0.02, Beta = 0.3, Sigma = 0.06), data = prices)

非常感谢任何帮助。

Answer 1

系数 Alpha 和 Sigma 之间存在相互关联。一个简单的解决方案是保持其中一个不变。也许重新制定方程式并替换为 Alpha 或 Sigma 会更好。

set.seed(1)
lnz_i <- function(TI, Alpha, Beta, Sigma) -TI*(Alpha*(1 - exp(-Beta*TI)) / (Beta) - (Sigma^2/2)*(1 - exp(-Beta*TI)) / (Beta)^2) - 0.02*(1 - exp(-Beta*TI)) / (Beta)
TI <- c(0.5, 2, 5, 10, 30)
prices <- data.frame(TI, zi=lnz_i(TI, 0.02, 0.3, 0.06)*runif(length(TI), .9, 1.1))

#Hold Alpha Fixed
Alpha <- 0.02 
nls(zi ~ lnz_i(TI, Alpha, Beta, Sigma), start = c(Beta=0.3, Sigma = 0.06), data = prices)
Alpha <- 0.04
nls(zi ~ lnz_i(TI, Alpha, Beta, Sigma), start = c(Beta=0.3, Sigma = 0.06), data = prices)
Alpha <- 0.1
nls(zi ~ lnz_i(TI, Alpha, Beta, Sigma), start = c(Beta=0.3, Sigma = 0.2), data = prices)
#Estimate for Beta is all the time 0.401 and residuals are at 0.003768,
#only Sigma is changing when Alpha is changed

#Hold Sigma Fixed
Sigma <- 0.06
nls(zi ~ lnz_i(TI, Alpha, Beta, Sigma), start = c(Alpha = 0.02, Beta = 0.3), data = prices)
Sigma <- 0.03
nls(zi ~ lnz_i(TI, Alpha, Beta, Sigma), start = c(Alpha = 0.02, Beta = 0.3), data = prices)

nls() : "Error in nlsModel(formula, mf, start, wts) : singular gradient matrix at initial parameter estimates "

nls() : "Error in nlsModel(formula, mf, start, wts) : singular gradient matrix at initial parameter estimates "

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