drc (version 1.6-0)

W1.4: The four-parameter Weibull functions

Description

'W1.4' and 'W2.4' provide the four-parameter Weibull functions, self starter function and names of the parameters.

Usage

W1.4(fixed = c(NA, NA, NA, NA), names = c("b", "c", "d", "e"))
  
  W2.4(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.

Value

• See weibull1.

Details

The equations for the mean functions are given at weibull1.

References

Seber, G. A. F. and Wild, C. J (1989) Nonlinear Regression, New York: Wiley & Sons (pp. 330--331).

See Also

Setting $c=0$ yields W1.3. A more flexible function, allowing fixing or constraining parameters, is available through weibull1.

Examples

## Fitting a four-parameter Weibull (type 1) model
terbuthylazin.m1 <- drm(rgr~dose, data = terbuthylazin, fct = W1.4())
summary(terbuthylazin.m1)

## Fitting a first-order multistage model
## to data from BMDS by EPA
bmds.ex1 <- data.frame(ad.dose=c(0,50,100), dose=c(0, 2.83, 5.67), num=c(6,10,19), total=c(50,49,50))

bmds.ex1.m1<-drm(num/total~dose, weights=total, data=bmds.ex1, fct=W2.4(fixed=c(1,NA,1,NA)), type="binomial")

plot(bmds.ex1.m1, ylim = c(0.05, 0.4), log = "")

modelFit(bmds.ex1.m1)  # same as in BMDS

summary(bmds.ex1.m1)  # same background estimate as in BMDS

logLik(bmds.ex1.m1)

## BMD estimate identical to BMDS result
## BMDL estimate differs from BMDS result (different method)
ED(bmds.ex1.m1, 10, ci="delta")

## Better fit

bmds.ex1.m2<-drm(num/total~dose, weights=total, data=bmds.ex1, fct=W1.4(fixed=c(-1,NA,1,NA)), type="binomial")
modelFit(bmds.ex1.m2)
summary(bmds.ex1.m2)
plot(bmds.ex1.m2, ylim = c(0.05, 0.4), log = "", add = TRUE, lty = 2)

ED(bmds.ex1.m2, 50, ci = "delta")