四参数自启动功能

Question

如何在不使用ssfpl的情况下创建四参数自启动功能？

我尝试使用以下公式创建自启动函数：

((bpX * ((bpY * x)^s2)) / (1 + ((bpY * x)^s2)))^(s1 / s2)

这是自启动功能：

SS_sample <- selfStart(
  ((bpX * ((bpY * x)^s2)) / (1 + ((bpY * x)^s2)))^(s1 / s2),

  model = function(x, breakPointX, breakPointY, slope1, slope2)
  {
    ifelse(x > breakPointX,
           (x - breakPointX) * slope2 + breakPointY,
           (x - breakPointX) * slope1 + breakPointY)
  },
  initial = function(mCall, data, LHS)
  {
    xy <- sortedXyData(mCall[["x"]], LHS, data)
    n <- nrow(xy)
    if (n < 4) {
      stop("TOO FEW DISTINCT INPUT VALUES TO FIT THE MODEL")
    }
    first <- seq(from=1, length.out=4)
    last <- seq(length.out=4, to=n)
    fit1 <- coefficients(lm.fit(cbind(1,xy[first,"x"]), xy[first,"y"]))
    fit2 <- coefficients(lm.fit(cbind(1,xy[last,"x"]), xy[last,"y"]))
    slope1 <- fit1[[2]]
    slope2 <- fit2[[2]]
    bpXY <- solve(cbind(-c(slope1,slope2), 1),
                  as.matrix(c(fit1[[1]], fit2[[1]])))
    breakPointX <- bpXY[1]
    breakPointY <- bpXY[2]
    structure(list(breakPointX, breakPointY, slope1, slope2),
              names=as.character(mCall[c("breakPointX", "breakPointY", "slope1", "slope2")]))
  },
  parameters = c("breakPointX", "breakPointY", "slope1", "slope2"))

当我尝试将函数拟合到nls模型上时，它总是以奇异的梯度错误结束。

我们非常感谢您的帮助。谢谢。