\HeaderA{SSlogis}{Logistic Model}{SSlogis}
\keyword{models}{SSlogis}
\begin{Description}\relax
This \code{selfStart} model evaluates the logistic
function and its gradient.  It has an \code{initial} attribute that
creates initial estimates of the parameters \code{Asym},
\code{xmid}, and \code{scal}.
\end{Description}
\begin{Usage}
\begin{verbatim}
SSlogis(input, Asym, xmid, scal)
\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 asymptote.
\item[\code{xmid}] a numeric parameter representing the \code{x} value at the
inflection point of the curve.  The value of \code{SSlogis} will be
\code{Asym/2} at \code{xmid}.
\item[\code{scal}] a numeric scale parameter on the \code{input} axis.
\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((xmid-input)/scal))}.  If all of
the arguments \code{Asym}, \code{xmid}, and \code{scal} 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}
Chick.1 <- ChickWeight[ChickWeight$Chick == 1, ]
SSlogis( Chick.1$Time, 368, 14, 6 )  # response only
Asym <- 368; xmid <- 14; scal <- 6
SSlogis( Chick.1$Time, Asym, xmid, scal ) # response and gradient
getInitial(weight ~ SSlogis(Time, Asym, xmid, scal), data = Chick.1)
## Initial values are in fact the converged values
fm1 <- nls(weight ~ SSlogis(Time, Asym, xmid, scal), data = Chick.1)
summary(fm1)

\end{ExampleCode}
\end{Examples}

