

   AAlltteerrnnaattiivvee AAssyymmppttoottiicc RReeggrreessssiioonn MMooddeell wwiitthh aann OOffffsseett

        SSasympOff(input, Asym, lrc, c0)

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

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

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

        lrc: a numeric parameter representing the natural loga-
             rithm of the rate constant.

         c0: a numeric parameter representing the `input' when
             response is zero.

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

        This `selfStart' model evaluates the alternative asymp-
        totic regression function and its gradient.  It has an
        `initial' attribute that will evaluate initial esti-
        mates of the parameters `Asym', `lrc', and `c0' for a
        given set of data.

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

        a numeric vector of the same length as `input'.  It is
        the value of the expression `Asym*(1 -
        exp(-exp(lrc)*(input - c0)))'.  If all of the arguments
        `Asym', `lrc', and `c0' are names of objects, as
        opposed to expressions or explicit numerical values,
        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( lme )
        data( CO2 )
        CO2.Qn1 <- CO2[CO2$Plant == "Qn1", ]
        SSasympOff( CO2.Qn1$conc, 32, -4, 43 )  # response only
        Asym <- 32
        lrc <- -4
        c0 <- 43
        SSasympOff( CO2.Qn1$conc, Asym, lrc, c0 ) # response and gradient

