SSweibull {stats}  R Documentation 
SelfStarting 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 
Drop 
a numeric parameter representing the change from

lrc 
a numeric parameter representing the natural logarithm of the rate constant. 
pwr 
a numeric parameter representing the power to which 
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 AsymDrop*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
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
})
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)
## 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)