.\" -*- nroff -*- generated from .Rd format
.BG
.FN SSfpl
.TL
Four-parameter Logistic Model
.DN
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.
.CS
SSfpl(input, A, B, xmid, scal)
.RA
.AG input
a numeric vector of values at which to evaluate the model.
.AG A
a numeric parameter representing the horizontal asymptote on
the left side (very small values of `input').
.AG B
a numeric parameter representing the horizontal asymptote on
the right side (very large values of `input').
.AG 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'.
.AG scal
a numeric scale parameter on the `input' axis.
.RT
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'.

.SA
`nls', `selfStart'
.EX
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
.KW models
.WR
