LL.3 {drc} | R Documentation |
'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(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"), ...) LL2.3(fixed = c(NA, NA, NA), names = c("b", "d", "e"), ...) LL2.3u(fixed = c(NA, NA, NA), names = c("b", "c", "e"), ...)
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 ). |
The three-parameter 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 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 multdrc
.
Christian Ritz
Finney, D. J. (1971) Probit Analysis, Cambridge: Cambridge University Press.
Related functions are LL.2
, LL.4
, LL.5
and the more general
llogistic
.
## 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)