\HeaderA{SSasymp}{Asymptotic Regression Model}{SSasymp}
\keyword{models}{SSasymp}
\begin{Description}\relax
This \code{selfStart} model evaluates the asymptotic regression
function and its gradient.  It has an \code{initial} attribute that
will evaluate initial estimates of the parameters \code{Asym}, \code{R0},
and \code{lrc} for a given set of data.
\end{Description}
\begin{Usage}
\begin{verbatim}
SSasymp(input, Asym, R0, lrc)
\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{R0}] a numeric parameter representing the response when
\code{input} is zero.
\item[\code{lrc}] a numeric parameter representing the natural logarithm of
the rate constant.
\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+(R0-Asym)*exp(-exp(lrc)*input)}.  If all of
the arguments \code{Asym}, \code{R0}, and \code{lrc} 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}}
\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
Lob.329 <- Loblolly[ Loblolly$Seed == "329", ]
SSasymp( Lob.329$age, 100, -8.5, -3.2 )  # response only
Asym <- 100
resp0 <- -8.5
lrc <- -3.2
SSasymp( Lob.329$age, Asym, resp0, lrc ) # response and gradient
getInitial(height ~ SSasymp( age, Asym, resp0, lrc), data = Lob.329)
## Initial values are in fact the converged values
fm1 <- nls(height ~ SSasymp( age, Asym, resp0, lrc), data = Lob.329)
summary(fm1)

\end{ExampleCode}
\end{Examples}

