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)