drc: weibull1 – R documentation

Become an expert in R — Interactive courses, Cheat Sheets, certificates and more!

weibull1

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).

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)

drc

Analysis of Dose-Response Curves

v3.0-1

GPL-2 | file LICENCE

Authors

Christian Ritz <ritz@bioassay.dk>, Jens C. Strebig <streibig@bioassay.dk>

Initial release

2016-08-25