R: Weibull model functions

weibull1 {drc} | R Documentation

## Weibull model functions

### Description

'weibull' and 'weibull2' provide a very general way of specifying Weibull dose response functions, under various constraints on the parameters.

### Usage

      weibull1(fixed = c(NA, NA, NA, NA),
               names = c("b", "c", "d", "e"),
               method = c("1", "2", "3", "4"),
               ssfct = NULL,
               fctName, fctText)

      weibull2(fixed = c(NA, NA, NA, NA),
               names = c("b", "c", "d", "e"),
               method = c("1", "2", "3", "4"),
               ssfct = NULL,
               fctName, fctText)

      weibull2x(fixed = rep(NA, 5),
               names = c("b", "c", "d", "e", "t0"),
               method = c("1", "2", "3", "4"),
               ssfct = NULL,
               fctName, fctText)

### 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 (should not contain ":"). The default is reasonable (see under 'Usage'). The order of the parameters is: b, c, d, e (see under 'Details').
`method` | character string indicating the self starter function to use.
`ssfct` | a self starter function to be used.
`fctName` | optional character string used internally by convenience functions.
`fctText` | optional character string used internally by convenience functions.

### Details

As pointed out in Seber and Wild (1989), there exist two different parameterisations of the Weibull model. They do not yield the same fitted curve for a given dataset (see under Examples).

One four-parameter Weibull model ('weibull1') is

f(x) = c + (d-c) \exp(-\exp(b(\log(x)-\log(e)))).

Another four-parameter Weibull model ('weibull2') is

f(x) = c + (d-c) (1 - \exp(-\exp(b(\log(x)-\log(e))))).

Both four-parameter functions are asymmetric with inflection point at the dose e.

### Value

The value returned is a list containing the non-linear function, the self starter function and the parameter names.

### Note

The functions are for use with the function `drm`.

### Author(s)

Christian Ritz

### References

Seber, G. A. F. and Wild, C. J (1989) Nonlinear Regression, New York: Wiley \& Sons (pp. 338–339).

### See Also

For convenience several special cases of the function 'weibull1' are available: `W1.2`, `W1.3` and `W1.4`.

Special cases of 'weibull2' are: `W2.2`, `W2.3` and `W2.4`.

These convenience functions should be used rather than the underlying functions `weibull1` and `weibull2`.

### Examples

    ## Fitting two different Weibull models
    ryegrass.m1 <- drm(ryegrass, fct = W1.4())
    plot(ryegrass.m1, conLevel=0.5)

    ryegrass.m2 <- drm(ryegrass, fct = W2.4())
    plot(ryegrass.m2, conLevel=0.5, add = TRUE, type = "none", col = 2)
    # you could also look at the ED values to see the difference

    ## A four-parameter Weibull model with b fixed at 1
    ryegrass.m3 <- drm(ryegrass, fct = W1.4(fixed = c(1, NA, NA, NA)))
    summary(ryegrass.m3)

    ## A four-parameter Weibull model with the constraint b>3
    ryegrass.m4 <- drm(ryegrass, fct = W1.4(), lowerl = c(3, -Inf, -Inf, -Inf),
    control = drmc(constr=TRUE))
    summary(ryegrass.m4)

[Package drc version 3.0-1 Index]