R: The two-parameter log-logistic function

LL.2 {drc} | R Documentation

## The two-parameter log-logistic function

### Description

'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.

### Usage

      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`.

### Author(s)

Christian Ritz

### 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!

[Package drc version 3.0-1 Index]