R: Self-Starting Nls Logistic Model

SSlogis {stats} | R Documentation

## Self-Starting Nls Logistic Model

### Description

This `selfStart` model evaluates the logistic function and its gradient. It has an `initial` attribute that creates initial estimates of the parameters `Asym`, `xmid`, and `scal`. In R 3.4.2 and earlier, that init function failed when `min(input)` was exactly zero.

### Usage

    SSlogis(input, Asym, xmid, scal)

### Arguments

`input` | a numeric vector of values at which to evaluate the model.
`Asym` | a numeric parameter representing the asymptote.
`xmid` | a numeric parameter representing the `x` value at the inflection point of the curve. The value of `SSlogis` will be `Asym/2` at `xmid`.
`scal` | a numeric scale parameter on the `input` axis.

### Value

a numeric vector of the same length as `input`. It is the value of the expression `Asym/(1+exp((xmid-input)/scal))`. If all of the arguments `Asym`, `xmid`, and `scal` are names of objects the gradient matrix with respect to these names is attached as an attribute named `gradient`.

### Author(s)

José Pinheiro and Douglas Bates

### See Also

`nls`, `selfStart`

### Examples

    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(tol = 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)

[Package stats version 4.0.5 Index]