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) 

REQUIRED 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.

SEE ALSO:

,

EXAMPLES:

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