R: Self-Starting Nls Gompertz Growth Model

SSgompertz {stats} | R Documentation

## Self-Starting Nls Gompertz Growth Model

### Description

This `selfStart` model evaluates the Gompertz growth model and its gradient. It has an `initial` attribute that creates initial estimates of the parameters `Asym`, `b2`, and `b3`.

### Usage

    SSgompertz(x, Asym, b2, b3)

### Arguments

`x` | a numeric vector of values at which to evaluate the model.
`Asym` | a numeric parameter representing the asymptote.
`b2` | a numeric parameter related to the value of the function at `x = 0`
`b3` | a numeric parameter related to the scale the `x` axis.

### Value

a numeric vector of the same length as `input`. It is the value of the expression `Asym*exp(-b2*b3^x)`. If all of the arguments `Asym`, `b2`, and `b3` are names of objects the gradient matrix with respect to these names is attached as an attribute named `gradient`.

### Author(s)

Douglas Bates

### See Also

`nls`, `selfStart`

### Examples

    DNase.1 <- subset(DNase, Run == 1)
    SSgompertz(log(DNase.1$conc), 4.5, 2.3, 0.7)  # response only
    local({  Asym <- 4.5; b2 <- 2.3; b3 <- 0.7
      SSgompertz(log(DNase.1$conc), Asym, b2, b3) # response _and_ gradient
    })
    print(getInitial(density ~ SSgompertz(log(conc), Asym, b2, b3),
                     data = DNase.1), digits = 5)
    ## Initial values are in fact the converged values
    fm1 <- nls(density ~ SSgompertz(log(conc), Asym, b2, b3),
               data = DNase.1)
    summary(fm1)
    plot(density ~ log(conc), DNase.1, # xlim = c(0, 21),
         main = "SSgompertz() fit to DNase.1")
    ux <- par("usr")[1:2]; x <- seq(ux[1], ux[2], length.out=250)
    lines(x, do.call(SSgompertz, c(list(x=x), coef(fm1))), col = "red", lwd=2)
    As <- coef(fm1)[["Asym"]]; abline(v = 0, h = 0, lty = 3)
    axis(2, at= exp(-coef(fm1)[["b2"]]), quote(e^{-b[2]}), las=1, pos=0)

[Package stats version 4.0.5 Index]