l3 {drc}R Documentation

The three-parameter logistic function

Description

'l3' provides the three-parameter logistic function where the lower limit is equal to 0.

'l3u' provides three-parameter logistic function where the upper limit is equal to 1, mainly for use with binomial/quantal response.

Usage

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

  l3u(fixed = c(NA, NA, NA), names = c("b", "c", "e"), useDer = FALSE)

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.
useDer logical. If TRUE derivatives are supplied, otherwise they are not supplied. Not implemented!

Details

The three-parameter logistic function with lower limit 0 is

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

The three-parameter logistic function with upper limit 1 is

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

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

Value

See logistic.

Note

This function is for use with the function multdrc.

Author(s)

Christian Ritz

References

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

See Also

Related functions are l2, l4, l5 and the more general logistic.

Examples


## Fitting model with lower limit equal 0
model1 <- multdrc(FA, fct=l3())
summary(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",
"control","w214","w214","w214","w214","w214"))
finney_ex19 <- data.frame(logdose, n, r, treatment)

## Fitting model where the lower limit is estimated
model2 <- multdrc(r/n~logdose, treatment, weights=n, data=finney_ex19, 
logDose=10, fct=l3u(), type="binomial", 
collapse=data.frame(treatment, 1, treatment))

summary(model2)
anova(model2)
plot(model2, conLevel=-1, ylim=c(0.1, 1.3))
abline(h=1, lty=2)

rm(model1, model2, n, r, treatment, finney_ex19)


[Package drc version 0.9-0 Index]