SSweibull {stats}  R Documentation 
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.
SSweibull(x, Asym, Drop, lrc, pwr)
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 
This model is a generalization of the SSasymp
model in
that it reduces to SSasymp
when pwr
is unity.
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
.
Douglas Bates
Ratkowsky, David A. (1983), Nonlinear Regression Modeling, Dekker. (section 4.4.5)
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)