R SSlogis 自啟動 NLS 邏輯模型

說明

這selfStart模型評估邏輯函數及其梯度。它有一個initial創建參數初始估計的屬性Asym,xmid， 和scal。在R3.4.2 及更早版本，該 init 函數在以下情況下失敗min(input)正好為零。

用法

SSlogis(input, Asym, xmid, scal)

參數

input	用於評估模型的數值向量。
Asym	表示漸近線的數字參數。
xmid	表示曲線拐點處的 x 值的數字參數。 SSlogis 的值將是 xmid 處的 Asym/2 。
scal	input 軸上的數字比例參數。

值

與 input 長度相同的數值向量。它是表達式 Asym/(1+exp((xmid-input)/scal)) 的值。如果所有參數 Asym 、 xmid 和 scal 都是對象的名稱，則相對於這些名稱的梯度矩陣將作為名為 gradient 的屬性附加。

例子

Chick.1 <- ChickWeight[ChickWeight$Chick == 1, ]
SSlogis(Chick.1$Time, 368, 14, 6)  # response only
local({
  Asym <- 368; xmid <- 14; scal <- 6
  SSlogis(Chick.1$Time, Asym, xmid, scal) # response _and_ gradient
})
getInitial(weight ~ SSlogis(Time, Asym, xmid, scal), data = Chick.1)
## Initial values are in fact the converged one here, "Number of iter...: 0" :
fm1 <- nls(weight ~ SSlogis(Time, Asym, xmid, scal), data = Chick.1)
summary(fm1)
## but are slightly improved here:
fm2 <- update(fm1, control=nls.control(tol = 1e-9, warnOnly=TRUE), trace = TRUE)
all.equal(coef(fm1), coef(fm2)) # "Mean relative difference: 9.6e-6"
str(fm2$convInfo) # 3 iterations


dwlg1 <- data.frame(Prop = c(rep(0,5), 2, 5, rep(9, 9)), end = 1:16)
iPar <- getInitial(Prop ~ SSlogis(end, Asym, xmid, scal), data = dwlg1)
## failed in R <= 3.4.2 (because of the '0's in 'Prop')
stopifnot(all.equal(tolerance = 1e-6,
   iPar, c(Asym = 9.0678, xmid = 6.79331, scal = 0.499934)))

## Visualize the SSlogis()  model  parametrization :
  xx <- seq(-0.75, 5, by=1/32)
  yy <- 5 / (1 + exp((2-xx)/0.6)) # == SSlogis(xx, *):
  stopifnot( all.equal(yy, SSlogis(xx, Asym = 5, xmid = 2, scal = 0.6)) )
  require(graphics)
  op <- par(mar = c(0.5, 0, 3.5, 0))
  plot(xx, yy, type = "l", axes = FALSE, ylim = c(0,6), xlim = c(-1, 5),
       xlab = "", ylab = "", lwd = 2,
       main = "Parameters in the SSlogis model")
  mtext(quote(list(phi[1] == "Asym", phi[2] == "xmid", phi[3] == "scal")))
  usr <- par("usr")
  arrows(usr[1], 0, usr[2], 0, length = 0.1, angle = 25)
  arrows(0, usr[3], 0, usr[4], length = 0.1, angle = 25)
  text(usr[2] - 0.2, 0.1, "x", adj = c(1, 0))
  text(     -0.1, usr[4], "y", adj = c(1, 1))
  abline(h = 5, lty = 3)
  arrows(-0.8, c(2.1, 2.9),
         -0.8, c(0,   5  ), length = 0.1, angle = 25)
  text  (-0.8, 2.5, quote(phi[1]))
  segments(c(2,2.6,2.6), c(0,  2.5,3.5),   # NB.  SSlogis(x = xmid = 2) = 2.5
           c(2,2.6,2  ), c(2.5,3.5,2.5), lty = 2, lwd = 0.75)
  text(2, -.1, quote(phi[2]))
  arrows(c(2.2, 2.4), 2.5,
         c(2.0, 2.6), 2.5, length = 0.08, angle = 25)
  text(      2.3,     2.5, quote(phi[3])); text(2.7, 3, "1")
  par(op)

作者

José Pinheiro and Douglas Bates

也可以看看

nls , selfStart