

   SSfpl {nls}                                  R Documentation

   FFoouurr--ppaarraammeetteerr LLooggiissttiicc MMooddeell

   DDeessccrriippttiioonn::

        This `selfStart' model evaluates the four-parameter
        logistic function and its gradient.  It has an `ini-
        tial' attribute that will evaluate initial estimates of
        the parameters `A', `B', `xmid', and `scal' for a given
        set of data.

   UUssaaggee::

        SSfpl(input, A, B, xmid, scal)

   AArrgguummeennttss::

      input: a numeric vector of values at which to evaluate
             the model.

          A: a numeric parameter representing the horizontal
             asymptote on the left side (very small values of
             `input').

          B: a numeric parameter representing the horizontal
             asymptote on the right side (very large values of
             `input').

       xmid: a numeric parameter representing the `input' value
             at the inflection point of the curve.  The value
             of `SSfpl' will be midway between `A' and `B' at
             `xmid'.

       scal: a numeric scale parameter on the `input' axis.

   VVaalluuee::

        a numeric vector of the same length as `input'.  It is
        the value of the expression `A+(B-A)/(1+exp((xmid-
        input)/scal))'.  If all of the arguments `A', `B',
        `xmid', and `scal' are names of objects, the gradient
        matrix with respect to these names is attached as an
        attribute named `gradient'.

   AAuutthhoorr((ss))::

        Jose Pinheiro and Douglas Bates

   SSeeee AAllssoo::

        `nls', `selfStart'

   EExxaammpplleess::

        library(nls)
        data( ChickWeight )
        Chick.1 <- ChickWeight[ChickWeight$Chick == 1, ]
        SSfpl( Chick.1$Time, 13, 368, 14, 6 )  # response only
        A <- 13; B <- 368; xmid <- 14; scal <- 6
        SSfpl( Chick.1$Time, A, B, xmid, scal ) # response and gradient
        getInitial(weight ~ SSfpl(Time, A, B, xmid, scal), data = Chick.1)
        ## Initial values are in fact the converged values
        fm1 <- nls(weight ~ SSfpl(Time, A, B, xmid, scal), data = Chick.1)
        summary(fm1)

