The three-parameter log-logistic function
'LL.3' and 'LL2.3' provide the three-parameter log-logistic function where the lower limit is equal to 0.
'LL.3u' and 'LL2.3u' provide three-parameter logistic function where the upper limit is equal to 1, mainly for use with binomial/quantal response.
LL.3(fixed = c(NA, NA, NA), names = c("b", "d", "e"), ...)
LL.3u(upper = 1, fixed = c(NA, NA, NA), names = c("b", "c", "e"), ...)
l3(fixed = c(NA, NA, NA), names = c("b", "d", "e"), ...)
l3u(upper = 1, fixed = c(NA, NA, NA), names = c("b", "c", "e"), ...)
LL2.3(fixed = c(NA, NA, NA), names = c("b", "d", "e"), ...)
LL2.3u(upper = 1, fixed = c(NA, NA, NA), names = c("b", "c", "e"), ...)upper |
numeric value. The fixed, upper limit in the model. Default is 1. |
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 |
The three-parameter log-logistic function with lower limit 0 is
f(x) = 0 + \frac{d-0}{1+\exp(b(\log(x)-\log(e)))}
or in another parameterisation
f(x) = 0 + \frac{d-0}{1+\exp(b(\log(x)-e))}
The three-parameter log-logistic function with upper limit 1 is
f(x) = c + \frac{1-c}{1+\exp(b(\log(x)-\log(e)))}
or in another parameterisation
f(x) = c + \frac{1-c}{1+\exp(b(\log(x)-e))}
Both functions are symmetric about the inflection point (e).
See llogistic.
This function is for use with the function drm.
Christian Ritz
Finney, D. J. (1971) Probit Analysis, Cambridge: Cambridge University Press.
## Fitting model with lower limit equal 0
ryegrass.model1 <- drm(rootl ~ conc, data = ryegrass, fct = LL.3())
summary(ryegrass.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",
"w214","w214","w214","w214","w214","w214"))
# Note that the control is included in one of the two treatment groups
finney.ex19 <- data.frame(logdose, n, r, treatment)
## Fitting model where the lower limit is estimated
fe19.model1 <- drm(r/n~logdose, treatment, weights = n, data = finney.ex19,
logDose = 10, fct = LL.3u(), type="binomial",
pmodels = data.frame(treatment, 1, treatment))
summary(fe19.model1)
modelFit(fe19.model1)
plot(fe19.model1, ylim = c(0, 1.1), bp = -1, broken = TRUE, legendPos = c(0, 1))
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