SSweibull               package:stats               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:

     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)

