\Header{selfStart.formula}{Construct Self-starting Nonlinear Models}
\keyword{models}{selfStart.formula}
\begin{Description}\relax
A method for the generic function `selfStart' for formula objects.\end{Description}
\begin{Usage}
\begin{verbatim}
selfStart(model, initial, parameters, template)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{model}] a nonlinear formula object of the form \code{\textasciitilde{}expression}.
\item[\code{initial}] a function object, taking three arguments: \code{mCall},
\code{data}, and \code{LHS}, representing, respectively, a matched
call to the function \code{model}, a data frame in
which to interpret the variables in \code{mCall}, and the expression
from the left-hand side of the model formula in the call to \code{nls}.
This function should return initial values for the parameters in
\code{model}.
\item[\code{parameters}] a character vector specifying the terms on the right
hand side of \code{model} for which initial estimates should be
calculated. Passed as the \code{namevec} argument to the \code{deriv}
function.
\item[\code{template}] an optional prototype for the calling sequence of the
returned object, passed as the \code{function.arg} argument to the
\code{deriv} function. By default, a template is generated with the
covariates in \code{model} coming first and the parameters in
\code{model} coming last in the calling sequence.
\end{ldescription}
\end{Arguments}
\begin{Value}
a function object of class \code{selfStart}, obtained by applying
\code{deriv} to the right hand side of the \code{model} formula. An
\code{initial} attribute (defined by the \code{initial} argument) is
added to the function to calculate starting estimates for the
parameters in the model automatically.\end{Value}
\begin{Author}\relax
Jose Pinheiro and Douglas Bates\end{Author}
\begin{SeeAlso}\relax
\code{\Link{selfStart.default}}, \code{\Link{deriv}}\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
library( nls )

## self-starting logistic model

SSlogis <- selfStart(~ Asym/(1 + exp((xmid - x)/scal)),
  function(mCall, data, LHS)
  {
    xy <- sortedXyData(mCall[["x"]], LHS, data)
    if(nrow(xy) < 4) {
      stop("Too few distinct x values to fit a logistic")
    }
    z <- xy[["y"]]
    if (min(z) <= 0) { z <- z + 0.05 * max(z) } # avoid zeroes
    z <- z/(1.05 * max(z))              # scale to within unit height
    xy[["z"]] <- log(z/(1 - z))         # logit transformation
    aux <- coef(lm(x ~ z, xy))
    parameters(xy) <- list(xmid = aux[1], scal = aux[2])
    pars <- as.vector(coef(nls(y ~ 1/(1 + exp((xmid - x)/scal)), 
                             data = xy, algorithm = "plinear")))
    value <- c(pars[3], pars[1], pars[2])
    names(value) <- mCall[c("Asym", "xmid", "scal")]
    value
  }, c("Asym", "xmid", "scal"))
\end{ExampleCode}
\end{Examples}

