SSweibull Self-Starting Nls 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$Time, 160, 115, -5.5, 2.5)   # response only
local({ Asym <- 160; Drop <- 115; lrc <- -5.5; pwr <- 2.5
  SSweibull(Chick.6$Time, Asym, Drop, lrc, pwr) # response _and_ gradient
})
## IGNORE_RDIFF_BEGIN
getInitial(weight ~ SSweibull(Time, Asym, Drop, lrc, pwr), data = Chick.6)
## IGNORE_RDIFF_END
## Initial values are in fact the converged values
fm1 <- nls(weight ~ SSweibull(Time, Asym, Drop, lrc, pwr), data = Chick.6)
summary(fm1)
## Data and Fit:
plot(weight ~ Time, Chick.6, xlim = c(0, 21), main = "SSweibull() fit to Chick.6")
ux <- par("usr")[1:2]; x <- seq(ux[1], ux[2], length.out=250)
lines(x, do.call(SSweibull, c(list(x=x), coef(fm1))), col = "red", lwd=2)
As <- coef(fm1)[["Asym"]]; abline(v = 0, h = c(As, As - coef(fm1)[["Drop"]]), lty = 3)