R: The three-parameter log-logistic function

LL.3 {drc} | R Documentation

## The three-parameter log-logistic function

### Description

'LL.3' and 'LL2.3' provide the three-parameter log-logistic function where the lower limit is equal to 0.

'LL.3u' and 'LL2.3u' provide three-parameter logistic function where the upper limit is equal to 1, mainly for use with binomial/quantal response.

### Usage

      LL.3(fixed = c(NA, NA, NA), names = c("b", "d", "e"), ...)

      LL.3u(upper = 1, fixed = c(NA, NA, NA), names = c("b", "c", "e"), ...)

      l3(fixed = c(NA, NA, NA), names = c("b", "d", "e"), ...)

      l3u(upper = 1, fixed = c(NA, NA, NA), names = c("b", "c", "e"), ...)

      LL2.3(fixed = c(NA, NA, NA), names = c("b", "d", "e"), ...)

      LL2.3u(upper = 1, fixed = c(NA, NA, NA), names = c("b", "c", "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 three-parameter log-logistic function with lower limit 0 is

f(x) = 0 + \frac{d-0}{1+\exp(b(\log(x)-\log(e)))}

or in another parameterisation

f(x) = 0 + \frac{d-0}{1+\exp(b(\log(x)-e))}

The three-parameter log-logistic function with upper limit 1 is

f(x) = c + \frac{1-c}{1+\exp(b(\log(x)-\log(e)))}

or in another parameterisation

f(x) = c + \frac{1-c}{1+\exp(b(\log(x)-e))}

Both functions are symmetric about the inflection point (e).

### Value

See `llogistic`.

### Note

This function is for use with the function `drm`.

### Author(s)

Christian Ritz

### References

Finney, D. J. (1971) Probit Analysis, Cambridge: Cambridge University Press.

### See Also

Related functions are `LL.2`, `LL.4`, `LL.5` and the more general `llogistic`.

### Examples

    ## Fitting model with lower limit equal 0
    ryegrass.model1 <- drm(rootl ~ conc, data = ryegrass, fct = LL.3())
    summary(ryegrass.model1)

    ## Fitting binomial response
    ##  with non-zero control response

    ## Example dataset from Finney (1971) - example 19
    logdose <- c(2.17, 2,1.68,1.08,-Inf,1.79,1.66,1.49,1.17,0.57)
    n <- c(142,127,128,126,129,125,117,127,51,132)
    r <- c(142,126,115,58,21,125,115,114,40,37)
    treatment <- factor(c("w213","w213","w213","w213",
    "w214","w214","w214","w214","w214","w214"))
    # Note that the control is included in one of the two treatment groups
    finney.ex19 <- data.frame(logdose, n, r, treatment)

    ## Fitting model where the lower limit is estimated
    fe19.model1 <- drm(r/n~logdose, treatment, weights = n, data = finney.ex19,
    logDose = 10, fct = LL.3u(), type="binomial",
    pmodels = data.frame(treatment, 1, treatment))

    summary(fe19.model1)
    modelFit(fe19.model1)
    plot(fe19.model1, ylim = c(0, 1.1), bp = -1, broken = TRUE, legendPos = c(0, 1))
    abline(h = 1, lty = 2)

[Package drc version 3.0-1 Index]