\HeaderA{SSasympOff}{Asymptotic Regression Model with an Offset}{SSasympOff}
\keyword{models}{SSasympOff}
\begin{Description}\relax
This \code{selfStart} model evaluates an alternative parametrization
of the asymptotic
regression function and the gradient with respect to those parameters.
It has an \code{initial}
attribute that creates initial estimates of the parameters
\code{Asym}, \code{lrc}, and \code{c0}.
\end{Description}
\begin{Usage}
\begin{verbatim}
SSasympOff(input, Asym, lrc, c0)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{input}] a numeric vector of values at which to evaluate the model.
\item[\code{Asym}] a numeric parameter representing the horizontal asymptote on
the right side (very large values of \code{input}).
\item[\code{lrc}] a numeric parameter representing the natural logarithm of
the rate constant.
\item[\code{c0}] a numeric parameter representing the \code{input} for which the
response is zero.
\end{ldescription}
\end{Arguments}
\begin{Value}
a numeric vector of the same length as \code{input}.  It is the value of
the expression \code{Asym*(1 - exp(-exp(lrc)*(input - c0)))}.  If all of
the arguments \code{Asym}, \code{lrc}, and \code{c0} are
names of objects, the gradient matrix with respect to these names is
attached as an attribute named \code{gradient}.
\end{Value}
\begin{Author}\relax
Jose Pinheiro and Douglas Bates
\end{Author}
\begin{SeeAlso}\relax
\code{\LinkA{nls}{nls}}, \code{\LinkA{selfStart}{selfStart}};
\code{example(SSasympOff)} gives graph showing the \code{SSasympOff}
parametrization, where \eqn{\phi_1}{} is \code{Asymp},
\eqn{\phi_3}{} is \code{c0}, and \eqn{t_{0.5}}{} is
\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
CO2.Qn1 <- CO2[CO2$Plant == "Qn1", ]
SSasympOff( CO2.Qn1$conc, 32, -4, 43 )  # response only
Asym <- 32; lrc <- -4; c0 <- 43
SSasympOff( CO2.Qn1$conc, Asym, lrc, c0 ) # response and gradient
getInitial(uptake ~ SSasympOff( conc, Asym, lrc, c0), data = CO2.Qn1)
## Initial values are in fact the converged values
fm1 <- nls(uptake ~ SSasympOff( conc, Asym, lrc, c0), data = CO2.Qn1)
summary(fm1)

\end{ExampleCode}
\end{Examples}

