\HeaderA{SSmicmen}{Michaelis-Menten Model}{SSmicmen}
\keyword{models}{SSmicmen}
\begin{Description}\relax
This \code{selfStart} model evaluates the Michaelis-Menten model and
its gradient.  It has an \code{initial} attribute that
will evaluate initial estimates of the parameters \code{Vm} and \code{K}
\end{Description}
\begin{Usage}
\begin{verbatim}
SSmicmen(input, Vm, K)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{input}] a numeric vector of values at which to evaluate the model.
\item[\code{Vm}] a numeric parameter representing the maximum value of the response.
\item[\code{K}] a numeric parameter representing the \code{input} value at
which half the maximum response is attained.  In the field of enzyme
kinetics this is called the Michaelis parameter.
\end{ldescription}
\end{Arguments}
\begin{Value}
a numeric vector of the same length as \code{input}.  It is the value of
the expression \code{Vm*input/(K+input)}.  If both
the arguments \code{Vm} and \code{K} 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}
PurTrt <- Puromycin[ Puromycin$state == "treated", ]
SSmicmen( PurTrt$conc, 200, 0.05 )  # response only
Vm <- 200; K <- 0.05
SSmicmen( PurTrt$conc, Vm, K ) # response and gradient
getInitial(rate ~ SSmicmen(conc, Vm, K), data = PurTrt)
## Initial values are in fact the converged values
fm1 <- nls(rate ~ SSmicmen(conc, Vm, K), data = PurTrt)
summary( fm1 )
## Alternative call using the subset argument
fm2 <- nls(rate ~ SSmicmen(conc, Vm, K), data = Puromycin,
           subset = state == "treated")
summary(fm2)

\end{ExampleCode}
\end{Examples}

