# 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`

. In R 3.4.2 and earlier, that
init function failed when `min(input)`

was exactly zero.

- 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`

.

##### See Also

##### Examples

`library(stats)`

```
# NOT RUN {
Chick.1 <- ChickWeight[ChickWeight$Chick == 1, ]
SSlogis(Chick.1$Time, 368, 14, 6) # response only
local({
Asym <- 368; xmid <- 14; scal <- 6
SSlogis(Chick.1$Time, Asym, xmid, scal) # response _and_ gradient
})
getInitial(weight ~ SSlogis(Time, Asym, xmid, scal), data = Chick.1)
## Initial values are in fact the converged one here, "Number of iter...: 0" :
fm1 <- nls(weight ~ SSlogis(Time, Asym, xmid, scal), data = Chick.1)
summary(fm1)
## but are slightly improved here:
fm2 <- update(fm1, control=nls.control(tol = 1e-9, warnOnly=TRUE), trace = TRUE)
all.equal(coef(fm1), coef(fm2)) # "Mean relative difference: 9.6e-6"
str(fm2$convInfo) # 3 iterations
# }
# NOT RUN {
<!-- %donttest -->
# }
# NOT RUN {
dwlg1 <- data.frame(Prop = c(rep(0,5), 2, 5, rep(9, 9)), end = 1:16)
iPar <- getInitial(Prop ~ SSlogis(end, Asym, xmid, scal), data = dwlg1)
## failed in R <= 3.4.2 (because of the '0's in 'Prop')
stopifnot(all.equal(tol = 1e-6,
iPar, c(Asym = 9.0678, xmid = 6.79331, scal = 0.499934)))
## Visualize the SSlogis() model parametrization :
xx <- seq(-0.75, 5, by=1/32)
yy <- 5 / (1 + exp((2-xx)/0.6)) # == SSlogis(xx, *):
stopifnot( all.equal(yy, SSlogis(xx, Asym = 5, xmid = 2, scal = 0.6)) )
require(graphics)
op <- par(mar = c(0.5, 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")
mtext(quote(list(phi[1] == "Asym", phi[2] == "xmid", phi[3] == "scal")))
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 = 3)
arrows(-0.8, c(2.1, 2.9),
-0.8, c(0, 5 ), length = 0.1, angle = 25)
text (-0.8, 2.5, quote(phi[1]))
segments(c(2,2.6,2.6), c(0, 2.5,3.5), # NB. SSlogis(x = xmid = 2) = 2.5
c(2,2.6,2 ), c(2.5,3.5,2.5), lty = 2, lwd = 0.75)
text(2, -.1, quote(phi[2]))
arrows(c(2.2, 2.4), 2.5,
c(2.0, 2.6), 2.5, length = 0.08, angle = 25)
text( 2.3, 2.5, quote(phi[3])); text(2.7, 3, "1")
par(op)
# }
```

*Documentation reproduced from package stats, version 3.5.0, License: Part of R 3.5.0*