LL.4 {drc} | R Documentation |

## The four-parameter log-logistic function

### Description

'LL.4' and 'LL2.4' provide the four-parameter log-logistic function, self starter function, names of the parameters and, optionally, first and second derivatives for a faster estimation.

### Usage

```
LL.4(fixed = c(NA, NA, NA, NA), names = c("b", "c", "d", "e"), ...)
l4(fixed = c(NA, NA, NA, NA), names = c("b", "c", "d", "e"), ...)
LL2.4(fixed = c(NA, NA, NA, NA), names = c("b", "c", "d", "e"), ...)
```

### Arguments

`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 |

### Details

The four-parameter log-logistic function is given by the expression

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

or in another parameterisation (converting the term `\log(e)`

into a parameter)

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

The 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 and Jens C. Streibig

### References

Seber, G. A. F. and Wild, C. J (1989) *Nonlinear Regression*, New York: Wiley \& Sons (p. 330).

### See Also

Setting `c=0`

yields `LL.3`

. See also `LL.5`

.

### Examples

```
spinach.m1 <- drm(SLOPE~DOSE, CURVE, data = spinach, fct = LL.4())
spinach.m1
```

*drc*version 3.0-1 Index]