R: Weibull growth curve model

SSweibull {nls} | R Documentation

## Weibull growth curve model

### Description

This `selfStart` model evaluates the Weibull model for growth curve data and its gradient. It has an `initial` attribute that will evaluate initial estimates of the parameters `Asym`, `Drop`, `lrc`, and `pwr` for a given set of data.

### Usage

    SSweibull(x, Asym, Drop, lrc, pwr)

### Arguments

`x` | a numeric vector of values at which to evaluate the model.
`Asym` | a numeric parameter representing the horizontal asymptote on the right side (very small values of `x`).
`Drop` | a numeric parameter representing the change from `Asym` to the `y` intercept.
`lrc` | a numeric parameter representing the natural logarithm of the rate constant.
`pwr` | a numeric parameter representing the power to which `x` is raised.

### Details

This model is a generalization of the `SSasymp` model in that it reduces to `SSasymp` when `pwr` is unity.

### Value

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

### Author(s)

Douglas Bates

### References

Ratkowsky, David A. (1983), Nonlinear Regression Modeling, Dekker. (section 4.4.5)

### See Also

`nls`, `selfStart`, `SSasymp`

### Examples

    data(ChickWeight)
    Chick.6 <- subset(ChickWeight, (Chick == 6) & (Time > 0))
    SSweibull(Chick.6$Time, 160, 115, -5.5, 2.5 )  # response only
    Asym <- 160; Drop <- 115; lrc <- -5.5; pwr <- 2.5
    SSweibull(Chick.6$Time, Asym, Drop, lrc, pwr)  # response and gradient
    getInitial(weight ~ SSweibull(Time, Asym, Drop, lrc, pwr), data = Chick.6)
    ## Initial values are in fact the converged values
    fm1 <- nls(weight ~ SSweibull(Time, Asym, Drop, lrc, pwr), data = Chick.6)
    summary(fm1)

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