The two-parameter log-logistic function

'LL.2' and 'LL2.2' provide the two-parameter log-logistic function where the lower limit is fixed at 0 and the upper limit is fixed at 1, mostly suitable for binomial/quantal responses.

LL.2(upper = 1, fixed = c(NA, NA), names = c("b", "e"), ...)

  l2(upper = 1, fixed = c(NA, NA), names = c("b", "e"), ...)

  LL2.2(upper = 1, fixed = c(NA, NA), names = c("b", "e"), ...)

Arguments

upper	numeric value. The fixed, upper limit in the model. Default is 1.
fixed	numeric vector. Specifies which parameters are fixed and at what value they are fixed. NAs for parameter that are not fixed.
names	a vector of character strings giving the names of the parameters. The default is reasonable.
...	Additional arguments (see llogistic).

Details

The two-parameter log-logistic function is given by the expression $$ f(x) = \frac{1}{1+\exp(b(\log(x)-\log(e)))}$$

or in another parameterisation $$ f(x) = \frac{1}{1+\exp(b(\log(x)-e))}$$

The model function is symmetric about the inflection point (\(e\)).

Value

See llogistic.

Note

This function is for use with the function drm.

See also

Related functions are LL.3, LL.4, LL.5 and the more general llogistic.

Examples

## Fitting a two-parameter logistic model 
##  to binomial responses (a logit model)
earthworms.m1 <- drm(number/total~dose, weights=total,
data = earthworms, fct = LL.2(), type = "binomial")

plot(earthworms.m1)  # not fitting at the upper limit!