SSasympOff               package:stats               R Documentation

Asymptotic Regression Model with an Offset

Description:

     This 'selfStart' model evaluates an alternative parametrization of
     the asymptotic regression function and the gradient with respect
     to those parameters. It has an 'initial' attribute that creates
     initial estimates of the parameters 'Asym', 'lrc', and 'c0'.

Usage:

     SSasympOff(input, Asym, lrc, c0)

Arguments:

   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 logarithm of the
          rate constant.

      c0: a numeric parameter representing the 'input' for which the
          response is zero.

Value:

     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,
     the gradient matrix with respect to these names is attached as an
     attribute named 'gradient'.

Author(s):

     Jose Pinheiro and Douglas Bates

See Also:

     'nls', 'selfStart'; 'example(SSasympOff)' gives graph showing the
     'SSasympOff' parametrization, where phi_1 is 'Asymp', phi_3 is
     'c0', and t_{0.5} is

Examples:

     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
     getInitial(uptake ~ SSasympOff( conc, Asym, lrc, c0), data = CO2.Qn1)
     ## Initial values are in fact the converged values
     fm1 <- nls(uptake ~ SSasympOff( conc, Asym, lrc, c0), data = CO2.Qn1)
     summary(fm1)

