SSweibull
SelfStarting Nls Weibull Growth Curve Model
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.
 Keywords
 models
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 they
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 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
.
References
Ratkowsky, David A. (1983), Nonlinear Regression Modeling, Dekker. (section 4.4.5)
See Also
Examples
library(stats)
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)
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