Four-parameter Logistic Model

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.

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.

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, as opposed to expressions or explicit numerical values, 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

Examples

library( lme )
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


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