R: Four-parameter Logistic Model

SSfpl {nls}

R Documentation

Four-parameter Logistic Model

Description

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

Usage

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

Arguments

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.

Value

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.

Author(s)

Jose Pinheiro and Douglas Bates

Examples

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)