drc (version 1.2-0)

LL.3: The three-parameter log-logistic function

Description

'LL.3' provides the three-parameter log-logistic function where the lower limit is equal to 0. 'LL.3u' provides three-parameter logistic function where the upper limit is equal to 1, mainly for use with binomial/quantal response.

Usage

LL.3(fixed = c(NA, NA, NA), names = c("b", "d", "e"), ...)
  
  LL.3u(fixed = c(NA, NA, NA), names = c("b", "c", "e"), ...)
  
  l3(fixed = c(NA, NA, NA), names = c("b", "d", "e"), ...)

  l3u(fixed = c(NA, NA, NA), names = c("b", "c", "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 llogistic).

Value

• See llogistic.

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 ($e$).

References

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

See Also

Related functions are LL.2, LL.4, LL.5 and the more general llogistic.

Examples

## Fitting model with lower limit equal 0
model1 <- multdrc(ryegrass, fct=LL.3())
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=LL.3u(), 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)