SSweibull                package: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)

