# SSlogis

##### Self-Starting Nls Logistic Model

This `selfStart`

model evaluates the logistic
function and its gradient. It has an `initial`

attribute that
creates initial estimates of the parameters `Asym`

,
`xmid`

, and `scal`

.

- Keywords
- models

##### Usage

`SSlogis(input, Asym, xmid, scal)`

##### Arguments

- input
- a numeric vector of values at which to evaluate the model.
- Asym
- a numeric parameter representing the asymptote.
- xmid
- a numeric parameter representing the
`x`

value at the inflection point of the curve. The value of`SSlogis`

will be`Asym/2`

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`Asym/(1+exp((xmid-input)/scal))`

. If all of the arguments`Asym`

,`xmid`

, and`scal`

are names of objects the gradient matrix with respect to these names is attached as an attribute named`gradient`

.

##### encoding

UTF-8

##### See Also

##### Examples

`library(stats)`

```
Chick.1 <- ChickWeight[ChickWeight$Chick == 1, ]
SSlogis(Chick.1$Time, 368, 14, 6) # response only
Asym <- 368; xmid <- 14; scal <- 6
SSlogis(Chick.1$Time, Asym, xmid, scal) # response and gradient
getInitial(weight ~ SSlogis(Time, Asym, xmid, scal), data = Chick.1)
## Initial values are in fact the converged values
fm1 <- nls(weight ~ SSlogis(Time, Asym, xmid, scal), data = Chick.1)
summary(fm1)
require(graphics)
xx <- seq(-0.5, 5, len = 101)
yy <- 5 / ( 1 + exp((2-xx)))
par(mar = c(0, 0, 3.5, 0))
plot(xx, yy, type = "l", axes = FALSE, ylim = c(0,6), xlim = c(-1, 5),
xlab = "", ylab = "", lwd = 2,
main = "Parameters in the SSlogis model")
usr <- par("usr")
arrows(usr[1], 0, usr[2], 0, length = 0.1, angle = 25)
arrows(0, usr[3], 0, usr[4], length = 0.1, angle = 25)
text(usr[2] - 0.2, 0.1, "x", adj = c(1, 0))
text(-0.1, usr[4], "y", adj = c(1, 1))
abline(h = 5, lty = 2, lwd = 0)
arrows(-0.8, 2.1, -0.8, 0, length = 0.1, angle = 25)
arrows(-0.8, 2.9, -0.8, 5, length = 0.1, angle = 25)
text(-0.8, 2.5, expression(phi[1]), adj = c(0.5, 0.5))
segments(2, 0, 2, 4.0, lty = 2, lwd = 0.75)
text(2, 4.0, expression(phi[2]), adj = c(0.5, 0))
segments(3, 5/(1+exp(-1)) + 0.025, 3, 4.0, lty = 2, lwd = 0.75)
arrows(2.3, 3.8, 2.0, 3.8, length = 0.08, angle = 25)
arrows(2.7, 3.8, 3.0, 3.8, length = 0.08, angle = 25)
text(2.5, 3.8, expression(phi[3]), adj = c(0.5, 0.5))
```

*Documentation reproduced from package stats, version 3.3, License: Part of R 3.3*

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