\HeaderA{SSasympOrig}{Asymptotic Regression Model through the Origin}{SSasympOrig}
\keyword{models}{SSasympOrig}
\begin{Description}\relax
This \code{selfStart} model evaluates the asymptotic regression
function through the origin and its gradient.  It has an
\code{initial} attribute that will evaluate initial estimates of the
parameters \code{Asym} and \code{lrc} for a given set of data.
\end{Description}
\begin{Usage}
\begin{verbatim}
SSasympOrig(input, Asym, 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.
\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*(1 - exp(-exp(lrc)*input))}.  If all of
the arguments \code{Asym} 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$Seed == "329", ]
SSasympOrig( Lob.329$age, 100, -3.2 )  # response only
Asym <- 100; lrc <- -3.2
SSasympOrig( Lob.329$age, Asym, lrc ) # response and gradient
getInitial(height ~ SSasympOrig(age, Asym, lrc), data = Lob.329)
## Initial values are in fact the converged values
fm1 <- nls(height ~ SSasympOrig( age, Asym, lrc), data = Lob.329)
summary(fm1)

\end{ExampleCode}
\end{Examples}

