# SSfpl

##### Self-Starting Nls Four-Parameter Logistic Model

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.

- Keywords
- models

##### 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`

.

##### See Also

##### Examples

`library(stats)`

```
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
print(getInitial(weight ~ SSfpl(Time, A, B, xmid, scal), data = Chick.1),
digits = 5)
## Initial values are in fact the converged values
fm1 <- nls(weight ~ SSfpl(Time, A, B, xmid, scal), data = Chick.1)
summary(fm1)
```

*Documentation reproduced from package stats, version 3.3.3, License: Part of R 3.3.3*

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