SSasymp
Asymptotic Regression Model

### Description

Evaluates asymptotic regression models. These are selfStart functions.

### Usage

    SSasymp(input, Asym, R0, lrc)
    SSasympOff(input, Asym, lrc, c0)
    SSasympOrig(input, Asym, lrc)

### Arguments

input | a numeric vector of values at which to evaluate the model.
Asym | a numeric parameter representing the upper asymptotic value of the model (as input goes to Inf).
R0 | a numeric parameter representing the response when input is zero. This argument is not in SSasympOrig, in which it is assumed to be zero.
c0 | a numeric parameter representing the input for which the response is zero. This is used instead of R0 in SSasympOff only.
lrc | a numeric parameter representing the natural logarithm of the rate constant.

### Details

Because these are selfStart functions, they have an attribute called "initial", which is a function that nls can call to compute reasonable starting values for fitting an asymptotic model to the input data.
Value

SSasymp | returns the value of the expression Asym+(R0-Asym)*exp(-exp(lrc)*input).
SSasympOrig | returns value of the expression Asym*(1 - exp(-exp(lrc)*input)).
SSasympOff | returns the value of the expression Asym*(1 - exp(-exp(lrc)*(input - c0))).

If all arguments except "input" are names of objects, then the gradient (Jacobian) matrix with respect to these names (evaluated at the values of those names) is attached as an attribute named gradient.
Note
These functions are intended for use in formulae given to the nls function or a similar functions.
See Also
nls, selfStart.
Examples

    SSasymp(-2:4, Asym=7, R0=2, lrc=.1)
    SSasympOff(-2:4, Asym=7, c0=1/exp(.1) * log(1-2/7), lrc=.1)
    with(list(Upper=7, ZeroPt=2, LogRate=.1), SSasymp(-2:4, Upper, ZeroPt, LogRate))
    tDat <- data.frame(
        effort = c(0, 1, 2, 5, 8, 10),
        result = c(2, 5.34, 6.45, 6.82, 6.98, 7))
    nls(result ~ SSasymp(effort, Upper, ZeroPt, LogRate), data=tDat)

Package stats version 6.1.5-18
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